Research Summary
Research Summary
The Power of Paradox: Some Recent Developments in Interactive Epistemology
Description
This survey describes a central paradox of game theory, viz. the Paradox of Backward Induction (BI). The paradox is that the BI outcome is often said to follow from basic game-theoretic principles--specifically, from the assumption that the players are rational. Yet, for many games, the BI prediction is both intuitively unsatisfying and experimentally invalid. We describe recent work on resolving this paradox. We suggest that the BI Paradox has proved to be very fruitful, in that its resolution has spurred the development of several new conceptual frameworks in game theory. These new frameworks are: (i) Belief Systems, which expand the traditional description of a game to include the players' beliefs, beliefs about beliefs ... about the game; (ii) Conditional and Lexicographic Probability Systems, which extend the usual Kolmogorov theory of probability to take account of probability-zero events; (iii) Complete Belief Systems, which are systems that contain every possible belief of each player; and (iv) Formal Languages, which are models of how the players reason about a game. The survey explains the role of each of these concepts in resolving the BI Paradox. We end with another paradox, akin to Russell's Paradox from set theory, that leads to an impossibility result on complete belief systems. This result points to an open area in game theory.