Allocation of Authority. Economics of Information and Contracts. Real and Formal Authority. Real and Formal Authority

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1 Allocation of Authority Economics of Information and Contracts Allocation of Authority Levent Koçesen Koç University In recent years many companies decentralized decision maing authority AT&T, GE, Eastman Koda, Fiat, Motorola, Xerox, Ford Lower level managers are better informed About consumer needs, competitors, technologies, maret opportunities, etc. But they may be biased in their decisions short-term biased, status quo biased, empire builders, etc. What is the optimal allocation of authority? Levent Koçesen (Koç University) Allocation of Authority / 37 Levent Koçesen (Koç University) Allocation of Authority / 37 Real and Formal Authority Real and Formal Authority Aghion, P. and J. Tirole (997), Real and Formal Authority in Organizations, Journal of Political Economy, 05, -9. How should decision maing authority be allocated within organizations? Formal authority: the right to decide Real authority: effective control over decisions Shareholders have formal authority but might have little control over board of directors CEO has formal authority but division manager might have real authority A principal who has formal authority can reverse agent s decision May refrain from doing so if. agent is better informed. objectives are not too dissimilar Could it be optimal to delegate formal authority to agent? This commits the principal not to reverse agent s decision Two potential benefits. Incentives agent is more willing to get informed. Participation reduces cost of agent s participation Cost: Principal looses control Levent Koçesen (Koç University) Allocation of Authority 3 / 37 Levent Koçesen (Koç University) Allocation of Authority 4 / 37

2 Real and Formal Authority Real and Formal Authority n 3 potential projects whose benefits are initially unnown Project yields private benefits B to the principal b to the agent No project: yields 0 benefit to both For each party at least one project yields sufficiently negative benefit If uninformed, no project is best Best project for principal benefit to principal B benefit to agent βb, β (0,] Best project for agent benefit to agent b benefit to principal αb, α (0,] α and β measure congruence between the preferences Principal and agent simultaneously choose how much effort to exert to learn about the projects If principal exerts effort E she learns the benefits of all projects with probability E pays cost CE If agent exerts effort e he learns the benefits of all projects with probability e pays cost ce Contracts are incomplete Projects cannot be described and contracted upon ex ante Initial contract can only specify which party has the formal authority Also assume that the agent is extremely ris averse Optimal compensation is a constant wage Levent Koçesen (Koç University) Allocation of Authority 5 / 37 Levent Koçesen (Koç University) Allocation of Authority 6 / 37 Real and Formal Authority If the party who has formal authority is informed she pics her favorite If she is not informed but the other party is, other party s preferred project is piced If neither is uninformed, no project is piced This is because for each there is one that is too bad P-formal authority (centralization): Principal has the formal authority If agent is informed he recommends a project If principal is informed she chooses her favorite project If she is not informed she follows agent s recommendation A-formal authority (delegation): Agent has the formal authority If principal is informed she recommends a project If agent is informed he chooses his favorite project If he is not informed he follows principal s recommendation Real and Formal Authority Therefore, payoffs are as follows Under P-formal authority Under A-formal authority up = EB +( E)eαB CE ua = Eβb+( E)eb ce up = eαb +( e)eb CE ua = eb+( e)eβb ce Levent Koçesen (Koç University) Allocation of Authority 7 / 37 Levent Koçesen (Koç University) Allocation of Authority 8 / 37

3 Real and Formal Authority Each party s choice of effort must be optimal given the other s effort choice Effort choices must constitute a Nash equilibrium In equilibrium each party s effort is a best response to the other s effort Best response correspondences: } BP(e) = argmax {EB +( E)αB CE E [0,] } BA(E) = argmax {Eβb+( E)eb ce e [0,] (E,e ) is a Nash equilibrium if E BP(e ) e BA(E ) best response correspondences intersect at (E,e ) Levent Koçesen (Koç University) Allocation of Authority 9 / 37 Real and Formal Authority: P-formal authority Under P-formal authority Principal maximizes payoff by choosing E We assume to guarantee interior solution FOC must hold: Or CE max EB +( E)eαB E [0,] b < c and B < C up = B eαb CE = 0 E E = B C ( αe) Levent Koçesen (Koç University) Allocation of Authority 0 / 37 Real and Formal Authority: P-formal authority Real and Formal Authority: P-formal authority Agent maximizes payoff by choosing e FOC must hold: Or ce max Eβb+( E)eb e [0,] ua = ( E)b ce = 0 e e = b c ( E) We can solve these two equations for e and E, but a graph is more useful Levent Koçesen (Koç University) Allocation of Authority / 37 E B C E = B C ( αe) e = b c ( E) A Nash Equilibrium 0 b 0 c Levent Koçesen (Koç University) Allocation of Authority / 37 P α e

4 Real and Formal Authority: P-formal authority Real and Formal Authority: A-formal authority What happens if principal s cost of effort decreases? E A B C 0 b e c α 0 Principal s probability of getting informed increases This discourages the agent from putting in more effort Under A-formal authority Payoffs are Show similarly that up = eαb +( e)eb CE ua = eb+( e)eβb ce E = B C ( e) and e = b c ( βe) Levent Koçesen (Koç University) Allocation of Authority 3 / 37 Levent Koçesen (Koç University) Allocation of Authority 4 / 37 Real and Formal Authority: A-formal authority E = B C ( e) and e = b c ( βe) P-formal authority vs A-formal authority E β E β A B C P A B C Nash Equilibrium 0 b 0 c Levent Koçesen (Koç University) Allocation of Authority 5 / 37 P α e 0 b α 0 c Under A-formal authority e is higher E is lower Since the P cannot overrule A s decision, A has more incentives to become informed Levent Koçesen (Koç University) Allocation of Authority 6 / 37 e

5 Participation View Agent s choices about clothing, hairdo, out-of-wor personal lifestyles has minor incentive effects but are very important for the agent Delegating decisions on these matters increases the agent s utility As a result the principal can decrease wage obtain control of other matters and still ensure the agent s participation To isolate these effects we will treat effort choices as fixed Participation View =,,...,m separate decisions Let x = when P eeps the control and x = 0 when he delegates Letting w be the wage, principal s payoff function [(E +( E)eα)x +(eα +( e)e)( x)]b w Can be written as Ee( α)bx w +A where A is expected payoff when x = 0 and independent of x Ee( α)b is how much payoff changes when control is transferred from agent to principal Payoff changes only if both are informed by amount ( α)b Levent Koçesen (Koç University) Allocation of Authority 7 / 37 Levent Koçesen (Koç University) Allocation of Authority 8 / 37 Participation View Agent s payoff function [(Eβ +( E)e)x +(e +( e)eβ)( x)]b +w Can be written as (D independent of x) Ee( β)bx +w +D Ee( β)b is how much payoff changes when control is transferred from principal to agent Payoff changes only if both are informed by amount ( β)b Participation View Principal s problem is to choose x, =,,...,m to maximize Ee( α)bx w +A subject to where ū is agent s outside option Ee( β)bx +w +D ū Individual rationality constraint must hold as equality Substituting in the constraint, principal s problem is max Ee( α)bx Ee( β)bx ū+a+d {x} Levent Koçesen (Koç University) Allocation of Authority 9 / 37 Levent Koçesen (Koç University) Allocation of Authority 0 / 37

6 Participation View Collecting terms, this equivalent to max Ee(( α)b ( β)b)x {x} Solution: and ( α)b > ( β)b x = ( α)b < ( β)b x = 0 Participation View Delegation is more liely for those decisions that matter little to the principal, because they involve little cash flow (B low) agent can be trusted (α high) that are important to the agent private benefits are high (b high) principal cannot refrain from hurting the agent (β low) Principal chooses control rights efficiently: Principal has control if resulting increase in her payoff is higher than the decrease in agent s payoff Otherwise agent has the control Levent Koçesen (Koç University) Allocation of Authority / 37 Levent Koçesen (Koç University) Allocation of Authority / 37 Empirical predictions: Participation View Empirical predictions: Incentive View Seems to fit empirical evidence on multi-division corporations Division manager s preferred decisions liely to be suboptimal for the firm (α low) when there are externalities on other divisions on future managers of the division on the firm as a whole Long-term investment decisions or those with an impact on the rest of the firm s image or strategy (such as advertising or bargaining with unions) have been ept centralized But managerial decisions concerning exclusively the division, such as manufacturing, purchasing, or short-term investment, are often delegated to the division Impact of payoff and congruence parameters is less clear-cut One unambiguous effect Increase in the agent s trust in the principal (β) maes centralization more desirable has no impact on the principal s payoff under centralization reduces the agent s effort under delegation Levent Koçesen (Koç University) Allocation of Authority 3 / 37 Levent Koçesen (Koç University) Allocation of Authority 4 / 37

7 Delegation and Communication Aghion & Tirole analyzes the effects of allocation of authority on the incentives to acquire information What if the agent is always better informed? Can the principal elicit that information? If actions cannot be contracted upon (contracts are incomplete) Principal will choose an expected payoff maximizing action given the agent s report Agent will choose his report strategically The amount of information that can be gathered from the agent depends on the divergence between the preferences Could it be better to delegate the decision maing authority? Delegation also becomes less attractive as the agent s preferences diverge more from the principal s It is not clear which one is better Delegation or Communication Cheap Tal When the agent s report (message) is payoff irrelevant tal is cheap First analyzed by Crawford, W. and J. Sobel (98), Strategic Information Transformation, Econometrica, 50, Delegation scenario analyzed by Dessein, W. (00), Authority and Communication in Organizations, Review of Economic Studies, 69, Levent Koçesen (Koç University) Allocation of Authority 5 / 37 Levent Koçesen (Koç University) Allocation of Authority 6 / 37 Cheap Tal Agent observes the state of the world θ [0,] Principal s prior on θ is uniform over [0,] Agent reports a message m R Principal observes m, updates her beliefs, and chooses an action y R Payoffs UP(y,θ) = (y θ) UA(y,θ) = (y (θ +b)) where b > 0 Agent always prefers a higher action Principal s best action is θ Agent s best action is θ +b Cheap Tal Is perfect communication possible? Suppose it is: type θ sends m(θ), where m is one-to-one Principal chooses θ after observing m(θ) But then type θ would prefer to send m(θ +b) Therefore, communication is necessarily noisy Crawford and Sobel showed that all equilibria are equivalent to partition equilibria Consider a partition of the type space into n intervals {[0,x),[x,x),...,[xn,]} All types in the same interval send the same message Levent Koçesen (Koç University) Allocation of Authority 7 / 37 Levent Koçesen (Koç University) Allocation of Authority 8 / 37

8 Cheap Tal: Partition Equilibria Let us start with a two-interval equilibrium All types in [0,x) send m All types in [x,] send m m After message m principal s beliefs are uniform over [0,x) and after m uniform over [x,] Principal s expected payoff for any E[θ] Cheap Tal: Partition Equilibria All types in [0,x) must prefer x/ to (x+)/ ( x ) ( x+ (θ +b) (θ+b)) for all θ [0,x) All types in [x,] must prefer (x+)/ to x/ FOC is She chooses E[(y θ) ] = y +ye[θ] E[θ ] y = E[θ] x after m and x+ after m ( x+ x ) (θ+b)) ( (θ +b) for all θ [x,] This implies that type x must be indifferent If she strictly preferred x over (x+)/, by continuity of payoff function in type, there would be a type θ > x who would strictly prefer x over (x+)/ Levent Koçesen (Koç University) Allocation of Authority 9 / 37 Levent Koçesen (Koç University) Allocation of Authority 30 / 37 Cheap Tal: Partition Equilibria Delegation or Communication Therefore or x (x+b) = x+ +(x+b) x = b Since we must have 0 < x <, such an equilibrium exists only if b < If P delegates, A chooses θ+b P s expected payoff (θ +b θ) dθ = b 0 If this condition holds, then a two-interval equilibrium exists Specify beliefs of P to be uniform over [0,x] for any message in [0,x) and uniform over [x,] for any message in [x,] Levent Koçesen (Koç University) Allocation of Authority 3 / 37 Levent Koçesen (Koç University) Allocation of Authority 3 / 37

9 Delegation or Communication Cheap Tal: Partition Equilibria If P communicates, her expected payoff where x = / b x ( x ) dθ ( x+ 0 θ θ) dθ x This can be calculated to be Delegation is better b 48 Dessein shows that delegation is better whenever b is such that informative equilibrium exists How informative can communication be? After message that is supposed to be sent by types in [xi,xi), P chooses xi +xi Boundary type xi must be indifferent between (xi +xi)/ and (xi +xi+)/ Or xi +xi xi +xi+ (xi +b) = +(xi +b) xi+ = xi xi +4b Levent Koçesen (Koç University) Allocation of Authority 33 / 37 Levent Koçesen (Koç University) Allocation of Authority 34 / 37 Cheap Tal: Partition Equilibria Can be written as xi+ xi = xi xi +4b Each interval s length must be 4b larger than the one before If the first interval has length ε and there are n intervals, we must have or ε+(ε+4b) +(ε+8b) + +(ε+(n )4b) = nε+4(++ (n ))b = nε+4 (n )n b = nε+n(n )b = For every n such that n(n )b <, there is ε > 0, such that there is an n-interval equilibrium Levent Koçesen (Koç University) Allocation of Authority 35 / 37 Cheap Tal: Partition Equilibria Most informative equilibrium is given by greatest integer n such that n(n )b < Applying the quadratic formula, this is the greatest integer smaller than ( ) + + b Decreases in b Smaller the agent s bias, more communicative the equilibrium As b 0, this goes to infinity Arbitrarily informative communication becomes possible There is always the completely uninformative babbling equilibrium Levent Koçesen (Koç University) Allocation of Authority 36 / 37

10 Allocation of Authority: Recap Benefits of delegation: Increases agent s incentives to gather information For tass that are important for A but not for P increases A s willingness to participate Allows use of local information Cost: If agent is biased, decisions are suboptimal Delegation is better when Bias is smaller P is less informed Cost of information gathering for P is higher Tas is important for A but not for P Levent Koçesen (Koç University) Allocation of Authority 37 / 37