Paradoxes of Interactive Rationality: A Unified View Extended Abstract

An increasingly popular, but of course not uncontroversial1, view is that “the fundamental insight of game theory [is] that a rational player must take into account that the players reason about each other in deciding how to play ” (Aumann and Dreze, 2008, pg. 81). Exactly how the players (should) incorporate the fact that they are interacting with other (actively reasoning) agents into their own decision making process is the subject of much debate. A variety of frameworks have been put forward to explicitly model the reasoning of rational agents in a strategic situation. Key examples include Brian Skyrms ’ models of “dynamic deliberation ” (Skyrms, 1990), Ken Binmore’s analysis of “eductive reasoning ” (Binmore, 1987), and Robin Cubitt and Robert Sugden’s “common modes of reasoning ” (Cubitt and Sugden, 2011).Although the details of these frameworks are quite different2, they share a common line of thought: Contrary to classical game theory, solution concepts are no longer the basic object of study. Instead, the “rational solutions ” of a game are the result of individual (rational) decisions in specific informational “contexts”. This perspective on the foundations of game theory is best exemplified by the so-called epistemic program in game theory (cf. Brandenburger, 2007). The central thesis here is that the basic mathematical model of a game should include an explicit parameter describing the players ’ informational attitudes. However, this broadly decision-theoretic stance does not simply reduce the question of decision-making in interaction to that of rational decision making in the face of uncertainty. Crucially, higher-order information (belief about beliefs, etc.) are key components of the informational context of a game: “In any particular structure, certain beliefs, beliefs about belief,..., will be present and others won’t be. So, there is an important implicit assumption behind the choice of a structure. This is that it is “transparent ” to the players that the beliefs in the type structure — and only those beliefs — are possible....The idea is that there is a “context ” to the strategic situation (eg., history, conventions, etc.) and this “context ” causes the players to rule out certain beliefs.