On Equilibrium in Pure Stategies in Games with Many Players

We introduce a framework of noncooperative games, allowing both countable sets of pure strategies and player types, in which players are characterized by their attributes and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash "-equilibrium in pure strategies that is ‘"-equivalent’. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. For the special case of at most a finite number of crowding attributes, we obtain analogs, for finite games, of purification results due to Pascoa (1993a,b,1998) for games with a continuum of players. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space.

LEARNING TO PLAY APPROXIMATE NASH EQUILIBRIA IN GAMES WITH MANY PLAYERS

We illustrate one way in which a population of boundedly rational individuals can learn to play an approximate Nash equilibrium. Players are assumed to make strategy choices using a combination of imitation and innovation. We begin by looking at an imitation dynamic and provide conditions under which play evolves to an imitation equilibrium ; convergence is conditional on the network of social interaction. We then illustrate, through example, how imitation and innovation can complement each other; in particular, we demonstrate how imitation can help a population to learn to play a Nash equilibrium where more rational methods do not. This leads to our main result in which we provide a general class of large game for which the imitation with innovation dynamic almost surely converges to an approximate Nash, imitation equilibrium.imitation ; best reply ; convergence ; Nash equilibrium

Social conformity and bounded rationality in arbitrary games with incomplete information: some first results

Intepret a set of players all playing the same pure strategy and all with similar attributes as a society. Is it consistent with self interested behaviour for a population to organise itself into a relatively small number of societies? By introducing the concept of approximate substitute players in non-cooperative games we are able to put a bound on the rationality of such social conformity for an arbitrary game and arbitrary number of societies

On the theory of equalizing differences Increasing abundances of types of workers may increase their earnings

The theory of equalising differences recognises that wage differentials may be required to equalise the attractiveness of alternative occupations. We examine this theory using the Conley/Wooders 'crowding types'' model. The crowding types model distinguishes between the tastes of a player and his crowding type, those attributes of the player that directly effect the well-being of other players in the same club - a player''s skill, productivity or personality are examples. A club can be interpreted as firm in which the job attributes are the club goods thus, the crowding types model, with its distinction between tastes and crowding types, provides a natural environment in which to study equalising differences. In contrast to results for earlier models, we demonstrate that even when small groups of players are strictly effective in a strong sense, an increase in the abundance of players of one crowding type can increase the core payoffs to players of that crowding type.cooperative game theory

Full agreement and the provision of threshold public goods

We report threshold public good experiments in which group members not only need to be individually willing to contribute enough to provide the public good but also have to agree with each other on what every group members should contribute. We find strong support to the hypothesis that full agreement increases successful provision, although it takes a few repetitions before group members can successfully coordinate. This is consistent with our theoretical results that full agreement works because it increases criticality of each individual decision. The existence of a focal point makes it possible for the group members to successfully coordinate.Public good, threshold, full agreement, focal point, experiment, coordination

Contagion and the emergence of convention in small worlds

We model a simple dynamic process in which boundedly rational agents learn through their interactions with others. Of interest is to study the process of contagion where by one action 'spreads throughout the population' and becomes conventional. We vary the network of player interaction between a regular lattice and a random network allowing us to model contagion in small world networks. Through simulation results we highlight the importance of network structure on both the possibility of contagion and the rate of contagion

Ransomware and reputation

open access articleRansomware is a particular form of cyber-attack in which a victim loses access to either his electronic device or files unless he pays a ransom to criminals. A criminal’s ability to make money from ransomware critically depends on victims believing that the criminal will honour ransom payments. In this paper we explore the extent to which a criminal can build trust through reputation. We demonstrate that there are situations in which it is optimal for the criminal to always return the files and situations in which it is not. We argue that the ability to build reputation will depend on how victims distinguish between different ransomware strands. If ransomware is to survive as a long term revenue source for criminals then they need to find ways of building a good reputation

The Law of Demand in Tiebout Economies

We consider a general equilibrium local public goods economy in which agents have two distinguishing characteristics. The first is 'crowding type', which is publicly observable and provides direct costs or benefits to the jurisdiction (coalition or firms) the agent joins. The second is taste type, which is not publicly observable, has no direct effects on others and is defined over private good, public goods and the crowding profile of the jurisdiction the agent joins. The law of demand suggests that as the quantity of a given crowding type (plummers, lawers, smart people, tall people, nonsmokers, for example) increases, the compensation that agents of that type receive should go down. We provide counterexamples, however, that show that some agents of a given crowding type might actually benefit when the proportion of agents with the same crowding type increases. This reversal of the law of demand seems to have to do with interaction effect between tastes and skills, something difficult to study without making these classes of characteristics distinct. We argue that this reversal seems to relate to the degree of difference between various patterns of tastes. In particular, if tastes are homogeneous, the law of demand holds.