Norms2: Norms About Norms

In this paper, I outline and defend the view that variations in compliance levels with one and the same norm represent different norms about following norms. In support of this claim, I first argue that classic game-theoretic accounts, which define norms as Nash equilibria of noncooperative games, typically consider variations in compliance levels as separate norms. After that, I suggest a more fine-grained, game-theoretic distinction that accounts for degrees of compliance with the same norm and I show how to incorporate such an account into a psychological framework. Finally, the paper examines what given degrees of compliance can reveal about the dynamics underlying the process of norm change. I will argue that they are indicators of different reactions to the introduction of new norms.

Refinement of acyclic-and-asymmetric payoff aggregates of pure strategy efficient Nash equilibria in finite noncooperative games by maximultimin and superoptimality

A theory of refining pure strategy efficient Nash equilibria in finite noncooperative games under uncertainty is outlined. The theory is based on guaranteeing the corresponding payoffs for the players by using maximultimin, which is an expanded version of maximin. If a product of the players’ maximultimin subsets contains more than one efficient Nash equilibrium, a superoptimality rule is attached wherein minimization is substituted with summation. The superoptimality rule stands like a backup plan, and it is involved if maximultimin fails to produce just a single refined efficient equilibrium (a metaequilibrium). The number of the refinement possible outcomes is 10. There are 3 single-metaequilibrium cases, 3 partial reduction cases, and 4 fail cases. Despite successfulness of refinement drops as the game gets bigger, pessimistic estimation of its part is above 54 % for games with no more than four players.

Pareto Optimality and Equilibria in Noncooperative Games

This chapter considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest of the Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the noncooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto-optimal Nash equilibria (PoNE) in mixed strategies is proven.