Roger B. Myerson

Optimal Auction Design

This paper considers the problem faced by a seller who has a single object to sell to one of several possible buyers, when the seller has imperfect information about how much the buyers might be willing to pay for the object. The sellers problem is to design an auction game which has a Nash equilibrium giving him the highest possible expected utility. Optimal auctions are derived in this paper for a wide class of auction design problems.

Efficient Mechanisms for Bilateral Trading

We consider bargaining problems between one buyer and one seller for a single object. The seller’s valuation and the buyer’s valuation for the object are assumed to be independent random variables, and each individual’s valuation is unknown to the other. We characterize the set of allocation mechanisms that are Bayesian incentive compatible and individually rational, and show the general impossibility of ex post efficient mechanisms without outside subsidies. For a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade, and mechanisms that can maximize a broker’s expected profit. Journal of Economic Literature Classification Number: 026.

INCENTIVE COMPATIBILITY AND THE BARGAINING PROBLEM

Collective choice problems are studied from the Bayesian viewpoint. It is shown that the set of expected utility allocations which are feasible with incentive-compatible mechanisms is compact and convex, and includes the equilibrium allocations for all other mechanisms. The generalized Nash solution proposed by Harsanyi and Selten is then applied to this set to define a bargaining solution for Bayesian collective choice problems.

Graphs and Cooperation in Games

Graph-theoretic ideas are used to analyze cooperation structures in games. Allocation rules, selecting a payoff for every possible cooperation structure, are studied for games in characteristic function form. Fair allocation rules are defined, and these are proven to be unique, closely related to the Shapley value, and stable for a wide class of games.

Optimal coordination mechanisms in generalized principal-agent problems

Abstract The general principal–agent problem is formulated, in which agents have both private information and private decisions, unobservable to the principal. It is shown that the principal can restrict himself to incentive-compatible direct coordination mechanisms, in which agents report their information to the principal, who then recommends to them decisions forming a correlated equilibrium. In the finite case, optimal coordination mechanisms can be found by linear programming. Some basic issues relating to systems with many principals are also discussed. Non-cooperative equilibria between interacting principals do not necessarily exist, so quasi-equilibria are defined and shown to exist.

Refinements of the Nash equilibrium concept

Seltens concept of perfect equilibrium for normal form games is reviewed, and a new concept of proper equilibrium is defined. It is shown that the proper equilibria form a nonempty subset of the perfect equilibria, which in turn form a subset of the Nash equilibria. An example is given to show that these inclusions may be strict.

Multistage Games with Communication

This paper considers multistage games with communication mechanisms that can be implemented by a central mediator. In a communication equilibrium, no player expects ex ante to gain by manipulating his reports or actions. A sequential communication equilibrium is a communication equilibrium with a conditional probability system under which no player could ever expect to gain by manipulation, even after zero-probability events. Codominated actions are defined. It is shown that a communication equilibrium is a sequential communication equilibrium if and only if it never uses codominated actions. Predominant communication equilibria are defined by iterative elimination of codominated actions and are shown to exist.

Conference structures and fair allocation rules

To describe how the outcome of a cooperative game might depend on which groups of players hold cooperative planning conferences, we study allocation rules, which are functions mapping conference structures to payoff allocations. An allocation rule is fair if every conference always gives equal benefits to all its members. Any characteristic function game without sidepayments has a unique fair allocation rule. The fair allocation rule also satisfies a balanced contributions formula, and is closely related to Harsanyis generalized Shapley value for games without sidepayments. If the game is superadditive, then the fair allocation rule also satisfies a stability condition.

A Theory of Voting Equilibria

A voting equilibrium arises when the voters in an electorate, acting in accordance with both their preferences for the candidates and their perceptions of the relative chances of various pairs of candidates being in contention for victory, generate an election result that justifies their perceptions. Voting equilibria always exist, and the set of equilibria can vary substantially with the choice of voting system. We compare equilibria under the plurality rule, approval voting, and the Borda system. We consider a candidate-positioning game and find that the plurality rule imposes little restriction on the position of the winning candidate in three-candidate races, while approval voting leads to a winner positioned at the median of the voter distribution. We contrast campaign activities intended to influence voter preferences with activities meant to influence only perceptions of candidate viability.

Incentives to Cultivate Favored Minorities under Alternative Electoral Systems

A simple model is used to compare, under different electoral systems, the incentives for candidates to create inequalities among otherwise homogeneous voters, by making campaign promises that favor small groups, rather than appealing equally to all voters. In this game model, each candidate generates offers for voters independently out of a distribution that is chosen by the candidate, subject only to the constraints that offers must be nonnegative and have mean 1. Symmetric equilibria with sincere voting are analyzed for two-candidate elections, and for multicandidate elections under rank-scoring rules, approval voting, and single transferable vote. Voting rules that can guarantee representation for minorities in multiseat elections generate, in this model, the most severely unequal campaign promises.