The Achievements and the Future of Game Theory: A User's Perspective Avinash Dixit Princeton University

Summary overview Some game-theoretic applications were analyzed implicitly for a long time. Game theory is now the dominant mode of thinking in most of economics, and increasing in other social sciences. There is a continuum from abstract theory to its uses, with feedback and contributions in both directions.

Previous implicitly game theoretic literature Cournot, Bertrand examples of Nash eq Edgeworth – shrinking contract curve Social choice theory Arrow, Sen International economics Johnson et al (tariff wars) Information economics Akerlof, Spence, Stiglitz

Increasingly explicit game theoretic formulations Gradual developments in 1960s and 70s: Debreu-Scarf (cooperative game) Wilson on auctions Hurwicz, Gibbard et al implementation Nash bargaining solution in labor Extensive form bargaining, Rubinstein etc. More in specific fields to follow

Microeconomics / IO More general, richer view of competition Many dimensions of competition strategy These other variables are not just shifters of demand and cost curves! Perfect competition is not price-taking, but “expected-utility-taking” Max { E[Π] | E[U]  U*}, = 0 by entry yields Max { E[U] | E[Π]  0} = U*

Industrial organization Repeated games Implicit collusion, chain-store paradox Feedback on theory – Abreu-Pearce-Stacchetti etc. Two-stage games Location and price competition Entry deterrence Commitment (Spence, Dixit) Private information (Milgrom-Roberts) Feedback on theory - refinements

Labor economics Bargaining (applications in many fields) Search theory Raiffa – Art and Science of Negotiation Search theory “Decisions” aspect of Luce and Raiffa Matching theory and applications Gale-Shapley, Roth et al Most of this field is empirical Game theorists can try to use the rich data

Macro and public economics Games with one large player (govt) and many small players (private sector) Mechanism design in taxation (Mirrlees) regulation (Baron-Myerson) Dynamic inconsistency, optimal policies with and without commitment, relation to perfectness. Role of delegation

International Economics Strategic trade policy Two-stage games of governments & firms Trade liberalization agreements Self-enforcement constraints Need for multilateral enforcement Monetary and fiscal cooperation Decision-making in common central bank Intraction with national fiscal authorities

Political economy Strategic voting, agenda manipulation Delegation May not be realistic in mass elections But important in committees, legislatures Rich data allows testing, estimation Delegation Why? Information acquisition Limits – Agency problems How – Mechanism design Power indexes Shapley-Shubik, Banzhaf

Institutions Attaining mutually preferred social outcomes as equilibria of individual behavior Formal (law) not perfect Non-governmental, self-enforcing, enforcement by third parties Creating focal points for assurance games Resolving prisoners’ dilemmas by Information collection and dissemination Enforcing good behavior: norms and sanctions

Order without law http://www.youtube.com/watch?v=eC4BN9kInXg

Law without order http://www.youtube.com/watch?v=H2JFL1Sk21Y

The next 50 years? Behavioral decision and game theory Comparing findings from lab and field, pinpointing the right mix in each context Degrees of credibility Can this be handled in Harsanyi model Games without common knowledge Incomplete awareness

Basic research is a never-ending process “Grook” by Piet Hein Problems worthy of attack Prove their worth by hitting back