Public communication is secure if a hostile third-party cannot decode the messages exchanged by the communicating parties. In Nash equilibrium, communication by computationally unbounded players cannot be secure. We assume complexity averse players, and show that a simple, secure, and costless communication protocol becomes available as the marginal complexity cost tends to zero.

The Prisoner's Dilemma (PD) exhibits a tragedy in this sense: if the players are fully informed and rational, they are condemned to a jointly dispreferred outcome. In this essay I address the following question: What feature of the PD's payoff structure is necessary and sufficient to produce the tragedy? In answering it I use the notion of a trembling-hand equilibrium. In the final section I discuss an implication of my argument, an implication which bears on the persistence of the problem (...) posed by the PD. (shrink)

Since the seminal paper of Nash (Proc Natl Acad Sci USA 36:48–49, 1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. In a recent paper of Pruzhansky (Int J Game Theory 40:351–365, 2011) it was shown that under fairy general conditions maximin strategies in completely mixed games can guarantee the same expected payoff as completely mixed Nash equilibrium strategies. Based on this finding, the current paper argues that maximin strategies have important properties. For instance, (...) maximin strategies may refine Nash equilibria in subjective mixed strategies. Further, Bayesian rationality of the players may favor maximin strategies more often than Nash equilibrium strategies. The paper concludes with several suggestions for further experimental research that may shed more light on whether maximin behavior can explain reality better than Nash equilibrium. (shrink)

Mixed-strategy equilibria are typically rather unstable in evolutionary game theory. “Monocyclic” games, such as Rock–Paper–Scissors, have only mixed equilibria, some of which are “stable” in the sense that sequential best replies lead to them; yet, even these games are prone to stable cycles under discrete-time simultaneous best replies, giving an unusual equilibrium-selection problem. This article analyzes such games in a random-utility setting where changing strategies is costly, and the speed of the dynamic is, thus, endogenous. The stochastically stable outcome is (...) determined by the cost of switching strategies; when switching costs are high, mixed equilibria are selected, whereas when switching costs are low, cycles are selected. (shrink)

We develop a theory of joint intention in contexts in which participants have mixed motives that can manifest in all-things-considered reasons to deviate from contributing to the desired project, e.g., contexts with collective action problems. Our theory is based on strategic equilibrium-based reasoning, which links the characterization of joint intention in terms of individual intentions with conditions on strategy profiles of the underlying strategic games. We use elements of equilibrium reasoning to construct a counterfactual account of joint intention in the (...) mixed-motive contexts, which extends the reach of the notion of joint intention considerably beyond that of previous formulations. (shrink)