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In the first chapter, we revisit the El Farol bar problem developed by Brian W. Arthur (1994) to investigate how one might best model bounded rationality in economics. We begin by modelling the El Farol bar problem as a market entry game and describing its Nash equilibria. Then, assuming agents are boundedly rational in accordance with a reinforcement learning model, we analyse long-run behaviour in the repeated game. In a single population of individuals playing the El Farol game, reinforcement learning predicts that the population is eventually subdivided into two distinct groups: those who invariably go to the bar and those who almost never do. We demonstrate that reinforcement learning predicts sorting in the El Farol bar problem. The second chapter considers the long-run behaviour of agents learning in finite population games with random matching. In particular we study finite population games composed of anti-coordination pair games. We find the set of conditions for the payoff matrix of the two-player game that ensures the existence of strict pure strategy equilibria in the finite population game. Furthermore, we suggest that if the population is sufficiently large and the two-player pair games meet certain criteria, then the long-run behaviour of individuals, learning in accordance with the Erev and Roth (1998) reinforcement model, asymptotically converges to pure strategy profiles of the population game. The third chapter investigates some of the theoretical predictions of learning theory in anti-coordination finite population games with random matching through laboratory experiments in economics. Previous data from experiments on anti-coordination games has focused on aggregate behaviour and has evidence that outcomes mimic the mixed strategy equilibrium. Here we show that in finite population anti-coordination games, reinforcement learning predicts sorting; that is, in the long run, agents play pure strategy equilibria where subsets of the population permanently play each available action. |
