For a finite game with perfect recall, a refinement of its set of Nash equilibria selects closed connected subsets, called solutions. Assume that each solution's equilibria use undominated strategies and some of its equilibria are quasi-perfect, and that all solutions are immune to presentation effects; namely, if the game is embedded in a larger game with more pure strategies and more players such that the original players' feasible mixed strategies and expected payoffs are preserved regardless of what other players do, then the larger game's solutions project to the original game's solutions. Then, for a game with two players and generic payoffs, each solution is an essential component of the set of equilibria that use undominated strategies, and thus a stable set of equilibria as defined by Mertens (1989).

A player's pure strategy is called relevant for an outcome of a game in extensive form with perfect recall if there exists a weakly sequential equilibrium with that outcome for which the strategy is an optimal reply at every information set it does not exclude. The outcome satisfies forward induction if it results from a weakly sequential equilibrium in which players' beliefs assign positive probability only to relevant strategies at each information set reached by a profile of relevant strategies. We prove that if there are two players and payoffs are generic, then an outcome satisfies forward induction if every game with the same reduced normal form after eliminating redundant pure strategies has a sequential equilibrium with an equivalent outcome. Thus in this case forward induction is implied by decision-theoretic criteria. Copyright 2009 The Econometric Society.

Journal Article A Bidding Model of Perfect Competition Get access Robert Wilson Robert Wilson Stanford University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 44, Issue 3, October 1977, Pages 511–518, https://doi.org/10.2307/2296904 Published: 01 October 1977 Article history Received: 01 October 1975 Accepted: 01 October 1976 Published: 01 October 1977

Unit and share auctions, 675.—Formulation, 676.—No proprietary information, 677.—Proprietary information, 680.—Discriminatory pricing, 686.—Vickrey auctions, 687.—Conclusion, 688.

Priority service offers a menu of contingent contracts for distribution of scarce supplies. Prices inducing customer's efficient self-selection are expectations of spot prices for comparable service. Customers' selections reveal the benefit of capacity expansion. Priority service can be implemented via sale of "priority points" or via provision of compensatory insurance. Several priority classes suffice to obtain most efficiency gains. Priority service Pareto dominates random rationing if excess revenue is refunded equally to customers.

We define the class of two‐player zero‐sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players, and a Nash equilibrium. If all discontinuities favor one player, then a value exists and that player has a maximin strategy. A property called payoff approachability implies existence of an equilibrium, and that the resulting value is invariant: games with the same payoffs at points of continuity have the same value and ɛ‐equilibria. For voting games in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his proposed policy, we provide tie‐breaking rules and assumptions about voters' preferences sufficient to imply payoff approachability. These assumptions are satisfied by generic preferences if the dimension of the space of policies exceeds the number of voters; or with no dimensional restriction, if the electorate is sufficiently large. Each Colonel Blotto game is a special case in which each candidate allocates a resource among several constituencies and a candidate gets votes from those allocated more than his opponent offers; in this case, for simple‐majority rule we prove existence of an equilibrium with zero probability of ties.

Liberalization of infrastructure industries presents classic economic issues about how organization and procedure affect market performance. These issues are examined in wholesale power markets. The perspective from game theory complements standard economic theory to examine effects on efficiency and incentives.

For each two-player game, a linear-programming algorithm finds a component of the Nash equilibria and a subset of its perfect equilibria that are simply stable in the sense that there are nearby equilibria for each nearby game that perturbs one strategy's probability or payoff more than others. Copyright 1992 by The Econometric Society.

[Priority service rations available supplies according to contracts that specify each customer's priority or rank order. This alternative market form can achieve most of the efficiency gains attributed to spot markets, which in some industries are expensive to organize. Rationing by priorities is prominent in capital-intensive industries with non-storable outputs, as well as in service-sector and make-to-order industries where service is queued or congested. This paper describes the role of priority service and sketches a basic model. The main topic is efficient implementation by public enterprises and by competitive firms.]