基于共识程度的双体博弈纳什均衡拓展研究

首先对一般双体博弈的策略进行拓展,提出共识纳什均衡的概念,并证明其存在性;根据共识程度的降低提出其他3种拓展形式——近似共识纳什均衡、局部共识纳什均衡和局部近似共识纳什均衡,并举例进行说明;然后,对各种均衡形式下的合作效率进行分析和比较。研究表明,共识纳什均衡的利益分配是基于信息本身——竞争环境的特殊形式,它是具有效率的。其他3种形式均衡的效率低于共识纳什均衡,但仍高于双体博弈纳什均衡。共识纳什均衡和其他3种形式的均衡为参与人组织更具效率的合作提供了渠道和理论解释。     

On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms

Consider nonempty finite pure strategy sets S₁,…,S_n, let S=S₁×⋅⋅⋅×S_n, let Ω be a finite space of “outcomes,” let Δ(Ω) be the set of probability distributions on Ω, and let θ: S→Δ(Ω) be a function. We study the conjecture that for any utility in a generic set of n‐tuples of utilities on Ω there are finitely many distributions on Ω induced by the Nash equilibria of the game given by the induced utilities on S. We give a counterexample refuting the conjecture for n≥3. Several special cases of the conjecture follow from well known theorems, and we provide some generalizations of these results.     

On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games

A game is better-reply secure if for every nonequilibrium strategy x^* and every payoff vector limit u^* resulting from strategies approaching x^*, some player i has a strategy yielding a payoff strictly above u_i^* even if the others deviate slightly from x^*. If strategy spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better-reply secure, then a pure strategy Nash equilibrium exists. Better-reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy Nash equilibria.     

Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information

This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing strategy (in the sense that higher types choose higher actions), a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite‐action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite‐action games that converges to a PSNE of the continuum‐action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first‐price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first‐price, multi‐unit, and all‐pay auctions; pricing games with incomplete information about costs; and noisy signaling games.