Frontiers of Game Theory.

• Author: Lipman, Barton L.

If one were asked to summarize the state of game theory today, one could do little better than to refer the questioner to this volume. To an extent I would not have thought possible in just 16 chapters, the editors have managed to cover essentially every "hot" issue in the area today through a series of excellent papers. Cooperative game theory, mechanism design/implementation, political economy, learning, equilibrium selection, experimental economics, axiomatic decision theory, and differential games are among the areas addressed. Oddly enough, I even enjoyed the editors' introduction. Though it is written by all three editors, one can easily recognize Binmore's sense of humor ("when they talk, gamesters talk a great deal, since they are a quarrelsome and unruly breed" - was this written by Binmore or P. G. Wodehouse?).

The papers emphasized below reflect my own biases, not a quality judgement - the quality of papers in this volume is not only remarkably high, but remarkably uniform. That noted, I was particularly fascinated by Camerer, Johnson, Rymon, and Sen's "Cognition and Framing in Sequential Bargaining for Gains and Losses." The authors gather unique data from their bargaining experiments: the order in which subjects analyze their information and how long they spend looking at each item. They compare the behavior of subjects taught and rewarded for backward induction with subjects who are simply playing the bargaining game. Surprisingly, many subjects in the latter group do not even look at the final period "pie" and so cannot possibly be backward inducting. Nor do they look at the end and then proceed to earlier stages. This work clearly suggests that interpretations of bargaining experiments based on adding "fairness" considerations but continuing to use standard backward induction arguments miss a large part of what is actually going on. The possibilities for further exploration of this technology seem very intriguing.

Several other papers provide fascinating introductions to recent developments. Moulin's "On the Fair and Coalition-Strategyproof Allocation of Private Goods" is a very readable exposition of strategyproof mechanisms and recent work on serial cost sharing in "On the Fair and Coalition-Strategyproof Allocation of Private Goods." Samuelson gives an interesting overview of much recent work in evolutionary game theory in the course of his "Does Evolution Eliminate Dominated Strategies?" Carlsson and van Damme survey...