It is thus controversial whether game theory is a substantive empirical theory that allows making predictions and to explain phenomena of interest. What appears to be less controversial is the understanding of game theory as the theory of rational choice in situations of strategic interaction. But appearances deceive. While most philosophers ans economists agree that there is a prescriptive reading of the theory, it is by no means clear what this reading amounts to.
If the two players play the strategies they most prefer, they end up in a situation they both dislike.
Given the players know this, to many observers playing ‘profligate/bekennen' does not seem so rational after all, especially when there seems to be a Pareto superior set of strategies available (frugal/ontkennen). Economists tend to respond that the Pareto superior set of strategies is only seemingly available. This is because if one of the players did play that strategy, the other would have a massive incentive not to do so himself, which is predicted by the first player who will therefore also stick with playing ‘profligate/bekennen'. But who is to say that this reasoning is compelling?
The folk of economics are economic agents. Economic agents haver preferences, which means that they can order the options available to them. When the value of the different options an agent faces depends on what other agents do, the agents are said to play a game, and they are referred to as players. Players in a game select among strategies. A strategy is a sequence op actions that tells a player what to do in response to other players' possible strategies.
Nash equilibrium: a set of strategies such that no player can improve het payoff by changing her strategy, given the strategies of the other player. The Nash equilibrium van be seen as the only sustainable outcome of rational negotiations in the absence of externally enforceable agreements.
A focal point is an equilibrium more likely to be chosen by the players because it seems special, natural or relevant to them. Focal points are a reasonable way to choose among equilibria, based in expectations of what people might do because of the existence of certain customs, habits or conventions. But it is not clear how to model focal points formally, which I why the theory remains undeveloped to this day. If considerations regarding focal points affect the payoffs, the focal-point strategy is also the Pareto dominant strategy. This is another refinement if the Nash equilibrium: if there are multiple Nash equilibria, choose the Pareto dominant outcome.
Any theory needs bridge principles in order to be applicable to empirical phenomena for theory testing, prediction and explanation. In game theory, bridge principles come in two types. Type one are assumptions about the form of people's utility functions. If people's utilities could be assumed to be strictly increasing in their own material gains and losses, one could use observations of material outcomes together with the tools of the theory to derive predictions. That simpla assumption is implausible, but nothing prevents economists from providing more complex functions in which other people's material gains and losses, and social and cultural norms play a role.
The other type of bridge principle are elicitation procedures. Here preferences are estimated without necessarily assuming that utility functions must have specific form.Game theory is not a theory of rationality, and thus game theoretic ‘explanations' are no rational- choice explanations. Game theorists are adamant that they do not intend to model the underlying decision processes of agents that are responsible for people's choices, and therefore they are no causal explanations either. For now let us conclude that as long as there are no more systematic insights into what bridge principles should be regarded as part of the core of the theory, game theory remains deeply problematic, both as a theory of rational choice as well as an explanatory theory.