Selection Equilibria of Higher-Order Games

Abstract

In applied game theory the modelling of each player’s intentions and motivations is a key aspect. In classical game theory these are encoded in the payoff functions. In previous work [2, 4] a novel way of modelling games was introduced where players and their goals are more naturally described by a special class of higher-order functions called quantifiers. We refer to these as higher-order games. Such games can be directly and naturally implemented in strongly typed functional programming languages such as Haskell [3]. In this paper we introduce a new solution concept for such higher-order games, which we call selection equilibrium. The original notion proposed in [4] is now called quantifier equilibrium. We show that for a special class of games these two notions coincide, but that in general, the notion of selection equilibrium seems to be the right notion to consider, as illustrated through variants of coordination games where agents are modelled via fixed-point operators. This paper is accompanied by a Haskell implementation of all the definitions and examples.