Behavioral perfect equilibrium in Bayesian games

Abstract

JEL classification: C72Keywords: Trembling hand perfect equilibrium Bayesian game with infinite type spaces Behavior strategy Second-price auction with incomplete information We develop the notion of perfect Bayesian Nash Equilibrium-perfect BNE-in general Bayesian games. We test perfect BNE against the criteria laid out by Kohlberg and Mertens (1986). We show that, for a focal class of Bayesian games, perfect BNE exists. Moreover, when payoffs are continuous, perfect BNE is limit undominated for almost every type. We illustrate the use of perfect BNE in the context of a second-price auction with interdependent values. Perfect BNE selects the unique pure strategy equilibrium in continuous strategies that separates types. Moreover, when valuations become independent, the equilibrium converges to the classical truthful dominant strategy equilibrium. We also show that less intuitive equilibria in which types are pooled are ruled out by our selection criterion. We further argue that standard selection criteria for second-price auctions have no bite here. Bidders have no dominant strategies, and the separating equilibrium is not sincere.

Comparing Crowdfunding Mechanisms: Introducing the Generalized Moulin-Shenker Mechanism

“…To weed out Bayesian-Nash equilibria in undominated strategies, an extension of (trembling-hand) perfect equilibrium to continuous games with incomplete information can be used (see e.g. Bajoori et al, 2016). More in particular, let 𝑚 ≡ min {𝑘 = 1, .…”

Equilibrium selection in interdependent value auctions

“…metric space, the weak topology on ∆ i is separable and metrizable with the weak (Prohorov) metric 6 , denoted by ρ w .…”

“…The above equilibrium concept may not exist even in finite games. DSPE is equivalent to strictly perfect equilibrium in finite normal form games 7 and we 6 See Aliprantis and Border [1]. Let µ and ν be two probability measures on a σ-field Σ.…”

“…We show that if each bidder believes that with a very small probability her opponent can bid according to the efficient bidding strategy, then overbidding or underbidding is not a best response. Bajoori et al (2016) [6], define the notion of Perfect BNE and apply this notion to an example in interdependent value auctions. In a Perfect BNE the strategies are robust against some slight perturbations of strategies.…”

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

“…To handle uncertainty of strategy taking in games, researchers also introduced the concepts of trembling hand perfect equilibrium, sequential equilibrium, and proper equilibrium . Nevertheless, these concepts still assume the probability of taking each single strategy can be accurately estimated (actually the main concern of the concepts is the probability of strategy mistaking).…”