Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. (Halpern, 2001) The jury is still out concerning the epistemic conditions for backward induction, the “oldest idea in game theory ” (Aumann, 1995, p. 635). Aumann (1995) and Stalnaker (1996) take conflicting positions in the debate: the former claims that common “knowledge ” of “rationality ” in a game of perfect information entails the backwardinduction solution; the latter that it does not. 1 Of course there is nothing wrong with any of their relevant formal proofs, but rather, as pointed out by Halpern (2001), there are differences between their interpretations of the notions of knowledge, belief, strategy and rationality. Moreover, as pointed out by Binmore (1987; 1996),

The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, a Theory of Play. In this paper we lay down the main components of such a theory, drawing on recent advances in the logical dynamics of actions, preferences, and information. We then show how this fine-grained perspective has already shed new light on the long-term dynamics of information exchange, as well as on the much-discussed question of extensive game rationality.

Recursive reasoning of the form what do I think that you think that I think (and so on) arises often while acting rationally in multiagent settings. Several multiagent decision-making frameworks such as RMM, I-POMDP and the theory of mind model recursive reasoning as integral to an agent’s rational choice. Real-world application settings for multiagent decision making are often mixed involving humans and human-controlled agents. In two large experiments, we studied the level of recursive reasoning generally displayed by humans while playing sequential general-sum and fixedsum, two-player games. Our results show that subjects experiencing a general-sum strategic game display first or second level of recursive thinking with the first level being more prominent. However, if the game is made simpler and more competitive with fixedsum payoffs, subjects predominantly attributed first-level recursive thinking to opponents thereby acting using second level of reasoning. Subsequently, we model the behavioral data obtained from the studies using the I-POMDP framework, appropriately augmented using well-known human judgment and decision models. Accuracy of the predictions by our models suggest that these could be viable ways for computationally modeling strategic behavioral data.

This paper focuses on the foundational role of interactive epistemology in the problem of generating plans for rational agents in multiagent settings. Interactive epistemology deals with the logic of knowledge and belief when there is more than one agent. In multiagent settings, we are interested in not only the agent’s knowledge of the state of the world, but also its belief over the other agents ’ beliefs and their beliefs over others’. We adopt a probabilistic approach for formalizing the epistemology. This paper attempts to answer the question of why we should study the interactive epistemology of agents within the context of multiagent planning. In doing so, it motivates the need for a more detailed examination of the epistemological foundations of multiagent planning. We conclude this paper with a framework for multiagent planning that explicitly constructs and reasons with nested belief structures.

Why were you initially drawn to game theory? I first saw game theory in a lecture given by Frank Hahn at Cambridge University, where I was an undergraduate. Hahn drew a 2 × 2 coordination game on the blackboard (see Figure 1) and explained that while the (2, 2) outcome was the ‘obvious ’ one in this game, the (1, 1) outcome was also possible. If Ann believes that Bob will play R, she will optimally play D. If Bob believes that Ann will play D, he will optimally play R. The outcome of the game depends on what the players believe about the game, not just on the ‘material ’ payoffs.

The literature on the epistemic foundations of game theory uses a variety of mathematical models to formalise talk about the players ’ beliefs about the game, beliefs about the rationality of the other players, beliefs about the beliefs of the other players, beliefs about the beliefs about the beliefs of the other players,

founded in 2000, and is based in the School of Economics at the

The focus for the Centre is research into individual and strategic decision‐making using a combination of theoretical and experimental methods. On the theory side, members of the Centre investigate individual choice under uncertainty, cooperative and non‐cooperative game theory, as well as theories of psychology, bounded rationality and evolutionary game theory. Members of the Centre have applied experimental methods in the fields of public economics, individual choice under risk and uncertainty, strategic interaction, and the performance of auctions, markets and other economic institutions. Much of the Centre's research involves collaborative projects with researchers from other departments in the UK and overseas.

Recursive reasoning of the form what do I think that you think that I think (and so on) arises often while acting rationally in multiagent settings. Previous investigations indicate that humans do not tend to ascribe recursive thinking to others. Several multiagent decisionmaking frameworks such as RMM, I-POMDP and the theory of mind model recursive reasoning as integral to an agent’s rational choice. Real-world application settings for multiagent decision making tend to be mixed involving humans and human-controlled agents. We investigate recursive reasoning exhibited by humans during strategic decision making. In a large experiment involving 162 participants, we studied the level of recursive reasoning generally displayed by humans while playing a sequential fixedsum, two-player game. Our results show that subjects experiencing a strategic game made more competitive with fixed-sum payoffs and tangible incentives predominantly attributed first-level recursive thinking to opponents. They acted using second level of reasoning exceeding levels of reasoning observed previously.