then mainstream Game Theory is extraordinarily general. It can offer some advice about what rational choice people should do in any social and economic interaction that can be described as a game: that is, rational people will/should play a strategy that is in a Nash equilibrium with others. This is an amazing claim and it explains why Game Theory can claim to be a general theory: it has something to say about any strategic interaction. Perhaps, not unsurprisingly, in view of such a claim, the Nash equilibrium solution concept has attracted considerable critical scrutiny. Since each action in a Nash equilibrium is the best for each player given the action of the others, the solution concept seems like a natural extension of rational choice reasoning to settings where dominance reasoning alone does not deliver a determinate outcome. In fact, it is now recognised that we must assume not only that each player is rational in the rational choice sense, but also that they each have common knowledge of rationality (that is, each knows that each is rational and knows that each knows that each knows that each is rational, and so on) and that each holds commonly aligned beliefs about what are rational inferences from any datum like a game. The additional assumptions are important. So long as a person knows through the common alignment of beliefs that there will be a unique inference about what rationality demands and if there is common knowledge of rationality in the rational choice model, then it follows that unique equilibrium must enjoy the property of being a Nash equilibrium. If it was not a Nash equilibrium, then someone would be expecting someone to do something that is not a best response to what others are doing and this contradicts the assumptions of rationality and common knowledge of rationality. Although the assumption of common knowledge of rationality is obviously strong, it has been relaxed in various models of bounded rationality that have become part of the mainstream canon. For example, Level-k models allow for individuals to have different levels of strategic sophistication (see Crawford et al 2013). Level 0 players don’t think strategically at all, they just choose. Level 1 players are strategic thinkers but they only take strategic thinking one stage by taking the best action given that they think they are playing against level 0 players. Level 2 players have thought through two levels of strategic thinking and take the best action given that they think they are playing against level 1, and so
then mainstream Game Theory is extraordinarily general. It can offer some advice about what rational choice people should do in any social and economic interaction that can be described as a game: that is, rational people will/should play a strategy that is in a Nash equilibrium with others. This is an amazing claim and it explains why Game Theory can claim to be a general theory: it has something to say about any strategic interaction. Perhaps, not unsurprisingly, in view of such a claim, the Nash equilibrium solution concept has attracted considerable critical scrutiny. Since each action in a Nash equilibrium is the best for each player given the action of the others, the solution concept seems like a natural extension of rational choice reasoning to settings where dominance reasoning alone does not deliver a determinate outcome. In fact, it is now recognised that we must assume not only that each player is rational in the rational choice sense, but also that they each have common knowledge of rationality (that is, each knows that each is rational and knows that each knows that each knows that each is rational, and so on) and that each holds commonly aligned beliefs about what are rational inferences from any datum like a game. The additional assumptions are important. So long as a person knows through the common alignment of beliefs that there will be a unique inference about what rationality demands and if there is common knowledge of rationality in the rational choice model, then it follows that unique equilibrium must enjoy the property of being a Nash equilibrium. If it was not a Nash equilibrium, then someone would be expecting someone to do something that is not a best response to what others are doing and this contradicts the assumptions of rationality and common knowledge of rationality. Although the assumption of common knowledge of rationality is obviously strong, it has been relaxed in various models of bounded rationality that have become part of the mainstream canon. For example, Level-k models allow for individuals to have different levels of strategic sophistication (see Crawford et al 2013). Level 0 players don’t think strategically at all, they just choose. Level 1 players are strategic thinkers but they only take strategic thinking one stage by taking the best action given that they think they are playing against level 0 players. Level 2 players have thought through two levels of strategic thinking and take the best action given that they think they are playing against level 1, and so
Hargreaves_Heap.docx