Commitment Problems 1 / 24

Transcription

1 Commitment Problems 1 / 24

2 A Social Dilemma You would take a good action if I would credibly promise to do something in the future 2 / 24

3 A Social Dilemma You would take a good action if I would credibly promise to do something in the future You can t trust me to follow through on my promise You take a different action as a result of the lack of trust that makes both of us worse off The ability to commit can create a Pareto improvement 2 / 24

4 Outline Costly Conflict Hold up 3 / 24

5 Why is there Conflict? 2 parties are having a dispute War Law Suit Strikes Bargaining over an externality Conflict/Bargaining failure is costly Bargain exists making both better off Propose: expected outcome of conflict Why is there costly conflict? 4 / 24

6 The Puzzle Value of the good: B Cost of conflict: c Probability party 1 wins: p If fight: U 1 = pb c U 2 = (1 p)b c Bargaining can yield the payoffs U 1 = pb U 2 = (1 p)b 5 / 24

7 Explaining Costly Conflict Overconfidence Indivisibility Commitment Problems 6 / 24

8 Negotiation and Conflict Divided Society with two groups: Large (L) Small (S) Large divides resources, B Keep share α and give 1 α to Small Small group can accept 1 α or start conflict Small group wins conflict with probability p 2 7 / 24

9 The Extensive Form Game L α S 8 / 24

10 The Extensive Form Game L α S W ar Acq 8 / 24

11 The Extensive Form Game L α S W ar Acq u L = (1 p 2 )B c u S = p 2 B c u L = αb u S = (1 α)b 8 / 24

12 Small s best-response No Conflict if: α < 1 p 2 + c B 9 / 24

13 Small s best-response No Conflict if: α < 1 p 2 + c B Conflict if: α > 1 p 2 + c B 9 / 24

14 Small s best-response No Conflict if: α < 1 p 2 + c B Conflict if: α > 1 p 2 + c B Indifferent if: α = 1 p 2 + c B 9 / 24

15 Large s best response Suppose Small chooses no conflict when indifferent Large wants to maximize her share Choose largest α 1 p 2 + c B Subgame Perfect Nash equilibrium: α = 1 p 2 + c B Conflict if α > 1 p 2 + c B ; No if α 1 p 2 + c B 10 / 24

16 Preemptive Conflict Same model but with an initial stage in which Small can start preemptive conflict Small wins preemptive conflict with probability p 1 > p 2 Idea is that Large is consolidating power 11 / 24

17 Preemptive Extensive Form Game L α S W ar Acq u L = (1 p 2 )B c u S = p 2 B c u L = αb u S = (1 α)b 12 / 24

18 Preemptive Extensive Form Game L α No S S W ar Acq u L = (1 p 2 )B c u S = p 2 B c P re W ar u L = αb u S = (1 α)b 12 / 24

19 Preemptive Extensive Form Game L α No S W ar Acq u L = (1 p 2 )B c u S = p 2 B c S P re W ar u L = αb u S = (1 α)b u L = (1 p 1 )B c u S = p 1 B c 12 / 24

20 Preemptive Attack Without preemptive conflict, Small s payoff is p 2 B c With preemptive conflict, Small gets p 1 B c Preemptive conflict is a best-response 13 / 24

21 A Pareto Improvement Suppose large could commit to proposing α = 1 p 1 Small would accept p 1 B > p 2 B c 14 / 24

22 A Pareto Improvement Suppose large could commit to proposing α = 1 p 1 Small would accept p 1 B > p 2 B c Large s Payoff Equilibrium: (1 p 1 )B c Suggested offer: (1 p 1 )B Small s Payoff Equilibrium: p 1 B c Suggested offer: p 1 B 14 / 24

23 Commitment Problem Large cannot commit to α = 1 p 1 Once Small foregoes preemptive attack, Large will renege and propose α = 1 p 2 + c B > 1 p 1 Small s payoff is then p 2 B c Thus, Small launches a preemptive attack 15 / 24

24 Examples Elites inside firm or organization blocking technological change Immigration reform Labor/Management dispute Negotiating with terrorists 16 / 24

25 Outline Costly Conflict Hold up 17 / 24

26 The Hold-up Problem Need up-front investment by an upstream producer After investment has taken place, bargaining power shifts to the downstream producer Leaders to under-investment of the upstream firm 18 / 24

27 A Model Upstream producer produces e units at cost c 2 e2 Downstream producer offers a price p per unit Values produce at α per unit Upstream producer can accept the offered price or use the product by itself Values the product at β < α per unit 19 / 24

28 Subgame Perfect Nash equilibrium Upstream will accept any price, p β Downstream will offer p = β Upstream effort will solve max e βe c 2 e2 Optimal choice of effort: e = β c 20 / 24

29 Utilitarian Optimum Utilitarian Planner solves: max e αe c 2 e2 Planner s choice of effort: e = α c Upstream firm underinvests 21 / 24

30 Examples of Hold-up Problems Supplier invests in infrastructure to build product to company s specifications An inventor selling an invention to user with highest valuation Users of specialized software A partnership where one partner invests in technical expertise and the other in client relations 22 / 24

31 Policy Responses to Commitment Problems Complete Contracts Decrease asset specificity Multiple Suppliers Vertical Integration Instill trust 23 / 24

32 Take Aways Commitment problems arise in dynamic settings due to shifting circumstances and incomplete contracting Give rise to inefficient behavior due to anticipation of future circumstances One solution is to create institutions Another solution is to add improve the contracting environment 24 / 24