A Game Theoretic Model of Deposit Contracts between the Bank and the Depositor - Extend Study on the Economic Analysis of Bank Run

Transcription

1 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 A Game Theoretic Moel of Deposit Contracts between the Bank an the Depositor - Exten Stuy on the Economic Analysis of Bank Run Jue-Shyan Wang & Chiao-Hsin Lin Department of Public Finance, National Chengchi University, Taiwan Corresponence: Jue-Shyan Wang, Professor, Department of Public Finance, National Chengchi University, 64, Tz-nan Roa, Sec, Wenshan, Taipei, 6, Taiwan jswang@nccueutw Receive: May 3, 04 Accepte: June 5, 04 Online Publishe: June 8, 04 oi:05430/ijfrv5n3p36 URL: Abstract This paper which extens the settings of Chen an Hasan (008) uses the game theoretic moel to focus on the topics of not only interactive policies between a bank an a epositor but bank runs Our stuy iscovers that epening on ifferent economic terms, the bank will probably propose two ifferent eposit contracts for epositor to accept or not After the acceptance of the eposit contract, the epositor will choose his withrawal time on the basis of ifferent liquiity preferences On the other han, bank runs occur only when one of the eposit contracts is propose an the negative information of the investment project is isclose to epositors Keywors: eposit contract, bank run, lener; signal, subgame perfect equilibrium Introuction Since the outbreak of the 997 Asian financial crisis, Hong Kong's Bank of East Asia (abbreviate to BEA) firstly suffere a bank run on September, 008 The event resulte from that people sprea malicious rumors about BEA s stability via Short Message Service (SMS) They tol the stories that BEA was encountering financial ifficulties because of the capital losses from investment in Lehman bons an American International Group (AIG) BEA was sai to be taken over by the government of Hong Kong Then Deputy Chief Executive of BEA issue a statement to clarify that the financial position of BEA was healthy an inicate that the rumor mongers were an attempt to unermine the stability of the financial system However, queues of epositors sought to withraw money from banks To solve the problem of bank run, the Chief Executive Officer of BEA clarifie again an the monetary authority of Hong Kong an the Financial Secretary were publicly behin BEA an guarantee the safety an sounness of the banking system This event thus ultimately subsie on September 5, 008 Some literature stuies about the issue of bank runs Diamon an Dybvig (983) point out that uner the eposit insurance system, bank will provie a superior eposit contract An such a eposit contract will be likely to prevent the occurrence of bank runs Chari an Jaganathan (988) fin that a bank run is inuce by averse information of the bank an the properties of information about the unerlying investment returns will influence the choice between eposit contracts or equity contracts in the absence of eposit insurance system Cooper an Ross (998) inicate that the banks cope with its eposit contract esign an investment ecisions accoring to the probability of bank run Besies, banks may provie a eposit contract to prevent bank runs But uner certain conitions, banks will choose a eposit with the risk of bank runs in orer to get a higher expecte return from the investments Chen (999) fins that on the conition of sequential service constrains an information asymmetry, the negative information from few banks may lea to large-scale panic run even to the collapse of the entire financial system Samartín (003) points out that bank runs are likely to be inuce by message or panic The eposit contract can be properly esigne to avoi bank runs But in some cases, the bank run may generate more benefits Golstein an Pauzner (005) moify the moel of Diamon an Dybvig (983) an fin that when the bank improves overall welfare an esigns a eposit contract, there will be a trae-off between the traing liquiity benefits an the costs of a bank run which are both brought from the eposit contract Alonso (996) analyzes the banking environment an fins that negative information about the investment performance of the bank may lea to bank runs Banks can prevent the occurrence of bank runs by esigning appropriate eposit contracts In some cases, avoiing bank runs can maximize the profits of the banks However, the occasional runs can be the optimum bank behavior in other cases Chen an Hasan (006) inicate that increasing the information transparency of banks will make higher incience of infectious runs, thereby Publishe by Scieu Press 36 ISSN E-ISSN

2 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 reucing epositors welfare They also point out that it can reuce the incience of runs if the eposit insurance system is esigne as that some epositors are fully insure an the others are partially insure Ennis an Keister (006) point out that the bank will provie a eposit contract with risk of runs when the incience of runs is very small In the case of not preventing bank runs, the bank will choose to hol an amount of reserves just equal to the eman of withrawal When the cost of early liquiating investment is high, a rise in the incience of runs may lea the bank to reuce the investment Chen an Hasan (008) use the symmetric pure-strategy subgame-perfect equilibrium to explain why the bank run is cause by epositors panic They note that in large-scale bank runs, the epositors were often unable to istinguish between goo banks an ba banks, so they swarm into banks to withraw Maea an Sakai (008) propose that basing on the lener of last resort theory (LLR), the original eposit contract resulting in bank runs may make allocation of funs more efficient because the central bank can provie liquiity supply for banks with insufficient liquiity The moel establishe by Chen an Hasan (008) assumes that the bank makes zero economic profit an is in a passive position Depositors make strategic ecisions against changes in the economic environment, while the bank oes not fight for its own interest This is more like a moel in which the epositor makes ecision by himself We moify the setting of Chen an Hasan into a competitive game moel in which there is an interaction between the bank an the epositor There are two types of epositors who will make ecisions for profit maximization separately We establish an extensive form game to solve for the equilibrium The conclusion is that accoring to ifferent economic terms, there will be two ifferent eposit contracts propose by the bank An the epositor will choose withrawal time in light of his liquiity preference Moreover, we fin that only one of these two contracts will bring about bank runs when the epositors receive the negative information of the investment project This paper can provie the other angle for viewing the issue of bank runs The structure of the paper is organize as follows: Section is the introuction Section escribes the settings of our moel Section 3 solves for the equilibrium Section 4 iscusses bank runs Concluing remarks are in Section 5 The Moel The settings of this paper are mainly base on an thereby moifie from the theoretical moel of Chen an Hasan (008) (Note ) Suppose there are three ecision-making ates (ate 0,, an ), besies a bank an a risk-neutral epositor existing in the society At perio 0, the epositor possesses a unit of enowment, then choosing whether he saves the enowment at the bank or not In the meanwhile, the bank provies a eposit contract (ie, the bank will gives the epositor when the contract matures at perio, yet the epositor will get, if he withrawals at perio in avance, an we continue the settings of Chen an Hasan (008), ) to attract the epositor If the epositor rejects the eposit contract, he still retains the original enowment, while the bank gets no return, an finally the game ens; if the epositor accepts the eposit contract, then the Bank may use the funs to carry out an investment plan This investment plan expires at perio, one of its expecte returns is R with probability p, yet the other is 0 with probability - p Suppose the plan s expecte rate of return pr, an if the bank liquiates the investment at perio, liquiation value of this investment plan is 0 In orer to iscuss the liquiity nees the epositor may face, assume that before the en of perio, the epositor will ivie into two types It means that he will become type with probability t, who must consume at perio to get utility, or will get no consumer utility at perio, while the remaining probability ( t) is type, who has no nee for liquiity at perio Assume that epositor oes not know his type at perio 0, an the epositor of type will receive a public signal s concerning p at perio The public signal s is of positive information H with probability, an is of negative information L with probability ( ), where (0,) The probability is ph /[ ( p)( q)] when the expecte return is R cause by s H, while p p( q)/[ p( q) ( p) q] is the probability when a return is R cause by s L, where L q (/,) is the precision of the signal s resulting in p L p p H (Note ) In Figure we isplay the above-escribe problems are in an extension-type game tree, which the action of the epositor withrawing in perio is a, while in perio is a On the other han, we o not introuce an insurance system in the iscussion, that is, once banks fails in the investment plan, the epositor will receive no rewar Accoring to the Publishe by Scieu Press 37 ISSN E-ISSN

3 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 above escription, if the epositor withraws at perio, the epositor gets, while the bank pays ; if the epositor withraws at perio, the bank will get p( R ), the epositor of type will get no utility because of not satisfie his liquiity nees, an the epositor of type will get ph an pl respectively base on the quality of the signal Figure The extension-type game tree of the moel In this paper, we use backwar inuction to solve for the subgame perfect equilibrium 3 The Equilibrium I, after the epositor of type receives the signal of positive information H, the expecte At the ecision point utility of his withrawal in perio (ie, taking action a ) is: p () H ( p)( q) Compare equation () with the utility of the epositor of type withrawing in perio (ie, taking action a ), we suppose /[ ( p)( q)] is not less than, meaning he will withraw in perio after receiving the signal of positive information H (Note 3) At the ecision point I, after the epositor of type receives the signal of negative information L, the utility of taking action a is: p( q) p L () p( q) ( ) Compare equation () with the utility of the epositor of type taking action a, we get when p( q ) /[ p( q) ( ) ] is more (less) than, he will withraw in perio () Then at the ecision point I, the utilities of the epositor of type taking action a an a are 0 an respectively, so he will take action a Nevertheless, at the ecision point I, we will iscuss it in two situations Situation is that the epositor of type chooses to withraw in perio after receiving the signal of negative information L, an in the meanwhile his expecte utility is ph ( ) Uner such situation, giving eposit contract the bank proposes, the expecte utility of the epositor accepting the contract (ie, taking action A ) is: t ( t)[ p ( ) ] H t ( t)[ ( ) ] (3) ( p)( q) Publishe by Scieu Press 38 ISSN E-ISSN

4 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 Compare equation (3) with the utility of rejecting the eposit contract (ie, taking action R ), we get when t ( t){[ ] /[ ( p)( q)] ( ) } is more (less) than, he will accept (reject) the contract Furthermore, situation is that the epositor of type chooses to withraw in perio after receiving the signal of negative information L, an in the meanwhile his expecte utility is ph ( ) pl Uner such situation, giving eposit contract the bank proposes, the expecte utility of the epositor accepting the contract (ie, taking action A ) is: t ( t)[ ph ( ) pl ] ( ) p( q) t ( p)( q) p( q) ( p) q ( t)[ ] (4) Compare equation (4) with the utility of rejecting the eposit contract, we get when t ( t) p {[ q] /[ ( p)( q)] [( )( q)] /[ p( q) ( p) q]} is more (less) than, he will accept (reject) the contract Finally, back to the ecision point I, the bank proposes a eposit contract to attract the epositor The epositor of type must withraw in perio, while after receiving negative information the epositor of type also withraws in perio uner situation, yet withrawing in perio uner situation From now on, we efine the expecte utility of the bank uner situation as V B : V t( ) ( t)[ p( R ) ( )( )] (5) B An the expecte utility of the bank uner situation is efine as V B : V t( ) ( t)[ p( R ) ( ) p( R )] (6) B ( ) ( ) ( ) Because the operation purpose of the From equation (6), we can simplify V B into t t p R bank is profit maximization, the following below is the subgame perfect equilibrium uner two situations to separately maximize V B an V B First, accoring to the assumption above, no matter uner which situation, at the ecision point I, the epositor of type will withraw in perio after receiving the signal of positive information H, that is p q /[ ( )( )] transpose into: ( p)( q) (7) If situation hols, at the ecision point I, the term of the epositor of type withrawing in perio after receiving the signal of negative information L is p( q ) /[ p( q) ( ) ], meaning: p( q) ( p) q (8) p( q) Combine equation (7) an equation (8), an we can arrange the inequality as: p( q) ( p) q ( p)( q) p( q) (9) It means the below conitions must be fulfille: We subtract the above two equations as: p( q) ( p) q ( p)( q) p( q) (0) Publishe by Scieu Press 39 ISSN E-ISSN

5 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 p( q) ( p) q ( p)( q) p( q) ( q) ( p) q ( q) ( p)( q) ( q) ( p)[ q ( q) ] ( q) q q, the term of p q q q Because of (/,) ( )[ ( ) ] /[ ] 0 is fulfille Next, at the ecision point I, given eposit contract, the term of the epositor accepting the contract is t ( t){[ ] /[ ( p)( q)] ( ) }, meaning: { [ ( t)] }[ ( p)( q)] () ( t) We make the following efinition for the convenience of mathematical symbols: () 0 { [ ( t)] } [ ( p )( q )] ( t) ( p)( q) p ( q ) ( p ) q p ( q ) Equation (9) an equation () combine, the terms that is not less than 0 an [, ] must be fulfille uner situation We can see the term of equation (0), 0, is efinitely fulfille in the foregoing Uner 0 efinitely fulfille, the terms, that must not less than 0 an [, ], make 0 0 have to be fulfille In the foregoing we suppose, so 0,an 0 0 will be fulfille Because the bank will lower as far as possible to reap more benefits, we get uner situation If situation hols, at the ecision point I, the term of the epositor of type withrawing in perio after receiving the signal of negative information L is p( q ) /[ p( q) ( ) ], meaning: p( q) ( p) q (3) p( q) Combine equation (7), equation (3) an the efinition of an, an we can get the term which must not less than Next, at the ecision point I, given eposit contract, the term of the epositor accepting the contract is t ( t) p {[ q] /[ ( p)( q)] [( )( q)] /[ p( q) ( p) q]}, meaning: ( t )( qp p q)(qp p q ) (4) ( t) p[ p(q )( q ) qq ] We efine the right sie of the in inequality (4) as 3, combine the constraint on, an get the term which must not less than max[, 3] Next, we substitute 3 an as into equation (4), then the results are equal to an more than separately, so 3 is obtaine Because must not less than max[, 3] an the bank will lower as far as possible, is obtaine uner situation Combine the above analysis of two situations, we can get the following lemma: Lemma Only one eposit contract of an is the eposit contract equilibrium Publishe by Scieu Press 40 ISSN E-ISSN

6 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 () : The utility of the bank is V B, the epositor of type withraws in perio, an the epositor of type at I withraws in perio, yet at I withraws in perio () : The utility of the bank is V B, the epositor of type withraws in perio, an the epositor of type at I an I both withraws in perio From Lemma we can know the ifference between the epositor ecisions is just that at the ecision point I, the epositor of type will withraw in perio uner situation, while withraw in perio uner situation Since is the protection offere to the epositor when the eposit contract expires at the en of perio Different will make the epositor of type have ifferent ecisions, is uner situation, yet uner situation is Because >, it makes the epositor of type have greater incentive to withraw in perio uner situation rather than withraw in perio uner situation Now we compare the size of V B an V B to etermine the bank s optimum choice on First subtract equation (6) from equation (5), an we get: (Note 4) ( ){ ( ) [ (3 )]} t p q q (5) q( q) As approaches 0, then equation (5) is less than Nevertheless, as approaches, then equation (5) is more than Besies, we ifferentiate equation (5) with respect to an get: ( t)[( p) q(3 p q)] ( t)[( p)( q ) q( q)] = >0 (6) q( q) q( q) Combine the interpretation of equation (5) an equation (6), an we can get the probability of the epositor receiving positive information is higher (lower), V B is likely to be more (less) than V B, meaning the bank is likely to choose to equal to ( ) Intuitively, although uner situation the bank will face the risk of the epositor of type withrawing early in perio after his reception of negative information, when the probability of the epositor receiving positive information is higher, the probability of the bank facing such a risk is lower Moreover, uner situation the amount of bank giving to the epositor who withrawals at perio is lower, so the bank prefers On the contrary, uner situation the amount of bank giving to the epositor who withrawals at perio is higher, but when the probability of the epositor receiving positive information is lower, the probability of the bank facing the risk of the epositor s withrawal at perio is higher, so the bank prefers Next, as p approaches 0, then we are unable to etermine whether equation (5) is positive or not(note 5) Nevertheless, as p approaches, then equation (5) is less than 0 We ifferentiate equation (5) with respect to p an get: ( t)(q) <0 (7) q( q) Combine the interpretation of equation (5) an equation (7), an we can get the probability p of the bank obtaining R is higher (lower), V B is likely to be less (more) than V B, meaning the bank is likely to choose to equal to ( ) Intuitively, uner situation the bank will face the risk of the epositor of type withrawing early in perio after the reception of negative information, an when the probability p of the bank obtaining R is lower, the probability of the bank facing such a risk is higher Moreover, uner situation the amount of bank giving to the epositor who withrawals at perio is lower, so the bank prefers On the contrary, uner situation the amount of bank giving to the epositor who withrawals at perio is higher, but when the probability p of the bank obtaining R is higher, the probability of the bank facing the risk of the epositor s withrawal at perio is lower, so the bank prefers On the other han, as q approaches /, then equation (5) is less than 0 Nevertheless, as q approaches, then equation (5) is more than 0 Next, we Publishe by Scieu Press 4 ISSN E-ISSN

7 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 ifferentiate equation (5) with respect to q an get: ( t)( p)[ q( q)] >0 (8) q ( q) Combine the interpretation of equation (5) an equation (8), an we can get the precision q of the signal s is higher (lower), V B is likely to be (more) less than V B, meaning the bank is likely to choose to equal to ( ) Intuitively, uner situation the bank will face the risk of the epositor of type withrawing early in perio after the reception of negative information, an when the precision q of the signal is higher, given the reception of positive information, the probability p H of the bank obtaining R is higher, so the probability of the bank facing such a risk is lower Moreover, uner situation the amount of bank giving to the epositor who withrawals at perio is lower, so the bank prefers On the contrary, uner situation the amount of bank giving to the epositor who withrawals at perio is higher, but when the precision q of the signal is lower, the probability of the bank facing the risk of the epositor s withrawal at perio is higher, so the bank prefers Integrate the above analysis, an we can obtain the following proposition : Proposition The bank eposit contract equilibrium arose from ifferent moel parameters are as follows: () When the probability of the epositor receiving positive information is higher (lower), V B is likely to be more (less) than V B, meaning the bank is likely to choose to equal to ( ) Moreover, as approaches 0, the bank will choose to equal to Nevertheless as approaches, the bank will choose to equal to () When the probability p of the bank obtaining R is higher (lower), V B is likely to be less (more) than V B, meaning the bank is likely to choose to equal to ( ) Moreover, as p approaches, the bank will choose to equal to (3) When the precision q of the signal s is higher (lower), V B is likely to be more (less) than V B, meaning the bank is likely to choose to equal to ( ) Moreover, as q approaches /, the bank will choose to equal to Nevertheless, as q approaches, the bank will choose to equal to The following below we use numerical simulation calculation to show the results of Proposition with the actual values of the parameters From the foregoing we learn that equation (5) cannot be etermine whether it is positive or not, an the part which the sign of equation (5) cannot be etermine is: Equation (9) is set to be zero, an the solution of is ( p) q[ q (3 p q)] (9) q( q) q( q) (q)( p) We get equation (0) is more than 0, then substitute = / 3 into equation (9), an get q is: (0) ( ) () p p p Next, we substitute = / into equation (9), an get q is: Finally, we substitute = / 3 into equation (9), an get q is: ( p p p ) () ( ) (3) p p p Publishe by Scieu Press 4 ISSN E-ISSN

8 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 Now we set that in Figure the horizontal axis shows p an the vertical axis shows q The curves from upper right to lower left in Figure separately represent the relationship of q an p when equation (), equation () an equation (3) are positive From equation (7) an equation (8) we can learn that p an q are respectively V is more likely to be greater positive or negative associate with equation (5) It means that as p is higher, B than V B, yet as q is higher, V B is more likely to be less than V B As a result, the part above the curve represents the scope of VB VB, an the part below the curve represents the scope of VB> V B Figure Besies, from Figure we can learn that with the increase of, the scope of VB VB is greater, meaning V B is more likely to be more than V B, which represents the bank is more likely to choose uner situation 4 Bank Run The setting of Chen an Hasan (008) is that as long as all the epositors withraw at perio, the bank run will occur, we exten their efinition From Lemma we can learn that eposit contract equilibrium involve uner situation an uner situation However in our moel, the bank run can only happen when which the epositor of type withraws at perio, an the epositor of type at I withraws at perio, while at I withraws at perio It makes two types of epositor may withraw at perio, an then leas a bank run to occur From the foregoing we learn that in Figure the part above the curve represents the scope of B B Because uner situation the utility V B of the bank is higher, it makes the bank to choose eposit contract, in turn triggering the occurrence of bank runs From Figure we know that bank runs occur when negative information is reveale, the incience of runs is On the other han, the part below the curve represents the scope of VB VB, an uner situation the utility V B of the bank is higher, so it makes the bank to choose eposit contract Bank runs will never happen uner such a situation, an the incience of runs is 0 This is Proposition : Proposition Only when the bank chooses an negative information is reveale, bank runs may happen Nevertheless, when the bank chooses, bank runs will never happen Meanwhile from Proposition we can arrange the following Corollary : Corollary When the probability of the epositor receiving positive information is higher, the probability p of the bank obtaining R is lower, an the precision q of the signal s is higher, the bank is likely to choose to equal to, therefore bank runs are easier to occur Proposition states that only when the bank chooses the contract may have two types of the epositor V V Publishe by Scieu Press 43 ISSN E-ISSN

9 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 both withraws at perio Nevertheless, the backgroun of economic conitions escribe by Corollary is the conition that the bank chooses the contract The intuitive reason of Corollary alreay has an associate iscussion before Proposition is inferre Intuitively, ue to >, uner the conition that the bank chooses the contract, because the benefits of withrawing until the next perio is relatively lower, the epositor receiving negative information tens to withrawing early at perio Next, we iscuss the similarities an ifferences between Chen an Hasan (008) an our moel concerne the situation of bank runs The former emphasizes there both are an iniviual minimum threshol success ratio of the investment plan whether the information is reveale or not When epositors expect the success ratio is less than the minimum threshol, the bank run phenomenon will occur Besies, the values of two minimum threshols are uncertain From another point of view, the bank runs we euce will occur when the bank proposes the eposit an the epositor receives negative message Known by Corollary, the lower the success ratio p of the investment plan, the more our moel is prone to meet with a bank run So the probability p of the bank obtaining R to both Chen an Hasan (008) an our moel makes an impact of the same irection on the occurrence of bank runs It is that the lower the probability p of the bank obtaining R, the lower the expecte return got from the epositor withrawing until the next perio, so there is a strong motivation for the epositor to withraw at perio In aition, the bank in our moel has policy selection to the eposit contract, an in response to ifferent economic conitions it will then select a eposit contract in avance to avoi a bank run However, the banking inustry is set to be perfectly competitive in Chen an Hasan (008) It is the isparity between our moel an Chen an Hasan (008) 5 Concluing Remark A bank runs is a phenomenon that the impacts of the panic in financial crisis or relevant negative information about the bank make epositors lose confience in the solvency of bank, an thus large numbers of epositors seek to withraw money from banks Because banks will turn their eposits into other investments, they o not always retain cash meaning that the eposits which banks keep are limite Once the bank encounters focuse an intensive withrawals, it will fall into crisis of liquiity shortage, probably leaing to operational ifficulties, even the risk of bankruptcy It is seen to be a suen an concentrate hazar Meanwhile, the bank run is highly contagious When a bank run occurs, if the bank oes not take timely measures or obtain other assistance, it often causes a larger-scale run, thereby resulting in the collapse of the banking system, hence the government will intervene when necessary as a result We expan the settings of Chen an Hasan (008), which originally assume that the bank is perfectly competitive, so the eposit contract is ecie by the economic environment We alter their moel an assume that the bank owns the initiative of participating in ecision making, an aims for maximizing its own benefits They originally assume numerous epositors jointly participate in ecision making, while there is only one epositor along with the bank as players in our moel, an the epositor ivie in two types of liquiity preference patterns will make ecisions for profit maximization separately Accoring to the interactive strategy game equilibrium of the bank an the epositor, the bank may propose two equilibria of the eposit contract for the epositor to accept it or not, an which eposit contract it proposes will epen on ifferent economic conitions the bank faces After the bank proposes the eposit contract an the epositor accepts it, the epositor in two ifferent types of liquiity preference will ecie when to withrawal in accorance with their respective eman We fin that bank runs will occur only when the bank offer one of the contracts an the epositor receives the negative message Future research can be extene to the introuction of a eposit insurance system to explore whether the eposit contract the bank provies will change, or uner the protection of the eposit insurance system, whether the epositor will postpone the moment of withrawal, even whether the occurrence of bank run will be put off On the other han, the research can also be extene to whether the egree to how fast the epositor receives negative information will affect the occurrence of bank runs an other issues We look forwar to the follow-up extension stuy to better unerstan the actual operation of the banking system an to reuce the likelihoo of bank runs Publishe by Scieu Press 44 ISSN E-ISSN

10 wwwscieuca/ijfr International Journal of Financial Research Vol 5, No 3; 04 References Alonso, I (996) On avoiing bank runs Journal of Monetary Economics, 37, Chari, V V, & R Jaganathan (988) Banking Panics, Information, an Rational Expectations Equilibrium Journal of Finance, 43, Chen, Y (999) The Role of the First Come, First Serve Rule an Information Externalities Journal of Political Economy, 07, Chen, Y, & I Hasan (006) The Transparency of the Banking System an the Efficiency of Information-Base Bank Runs Journal of Financial Intermeiation, 5, Chen, Y, & I Hasan (008) Why Do Bank Run Look Like Panic? A New Explanation Journal of Money, Creit an Banking, 40, -3, Cooper, R, & T W Ross (998) Bank Runs: Liquiity Costs an Investment Distortions Journal of Monetary Economics, 4, Diamon, D W, & P H Dybvig (983) Bank Runs, Deposit Insurance an Liquiity Journal of Political Economy, 9, Ennis, H M, & T Keister (006) Bank Runs an Investment Decisions Revisite Journal of Monetary Economics, 53, Golstein, I, & A Pauzner (005) Deman-Deposit Contracts an the Probability of Bank Runs Journal of Finance, 60, Maea, Y, & Y Sakai (008) Microeconomic Founation of Lener of Last Resort from the Viewpoint of Payments Japanese Economic Review, 59, Samartín, M (003) Shoul bank runs be prevente? Journal of Banking & Finance, 7, Notes Note The biggest ifference between our paper an Chen an Hasan (008) is that the bank in our moel can actively choose the size of an to maximize its profits, an only one epositor is set to ivie into two types to iscuss his interactive ecisions with the bank Nevertheless, the banking system in Chen an Hasan (008) is perfectly competitive, so the bank s ecision making is relevant to market zero-profit conition, an there are large numbers of the epositors who ivie into two types Note The settings of p H an p L are similar with Chen an Hasan (008) Note 3 The assumption that the epositor of type chooses to withraw at perio after receiving positive information, is mainly to avoi the conition that two types of the epositor both withraw at perio Note 4 The values of the equations analyze below are all establishe uner the assumption of q (/,) Note 5 As p approaches 0, the numerator of equation (5) approaches ( t )[ ( q ) q ( q )( )] ; meanwhile, as approaches 0, equation (5) is less than 0; as approaches, equation (5) is more than 0 As a result, as p approaches 0, whether equation (5) is positive or not epens on other parameters Publishe by Scieu Press 45 ISSN E-ISSN