Such restrictions are the norm rather than the exception in dynamic models in economics. Moreover, these types of equilibrium selection arguments are not restricted to repeated game. Along with other restrictions, the restriction to certain simple strategies, such as the grim trigger strategy, is commonly used. This multiplicity of equilibria has led some researchers, both theoretical and applied, to restrict attention to certain equilibria. It demonstrates that any individually rational and feasible payoff vector of a two-player normal form game is a perfect equilibrium outcome of the repeated game, when the discount factor is sufficiently near one. In addition, putting the complexity problem in the wider context, one of the main benchmark results in the theory of repeated games is the folk theorem. Thus, it is reasonable to consider the complexity of the strategy (the idea that the assumption of fully, or unboundedly, rational players is unrealistic is not new see, e.g., ). This is usually the case in repeated games-at every stage, players are playing a history (in-)dependent game and therefore the set of all strategies can be huge. While this latter assumption may seem innocuous in a model where few strategies are available to each player, it may be criticized as being unrealistically rational in more complex models where a theoretical definition of strategy leads to a strategy set that contains a large number of choices, many of which are impractically complex. Generally, in the literature, it is assumed that players can carry out any strategy in a specified strategy set, should they choose to play it. In every stage game, each player uses a mixed strategy (in order to avoid possible confusion, we point out that, as is standard in the literature, we consider mixed strategies so long as their support lies in the set of feasible pure strategies a possible interpretation of mixed strategies in games in general is that they are distributions of pure strategies in a population of potential players). Each plan of action (play) is an infinite sequence of pairs (for two-player games) or n-tuples (in the n-player game) of strategies in each stage game. In such games, a strategy is a set of history-contingent plans of action. ![]() In particular, repeated games play the central role in models of the long-term competition in economic theory and modeling interactions which are repeated frequently. Many social (economic, political, etc.) interactions have been modeled as formal games.
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