Games, Information, and Politics: Applying Game Theoretic Models to Political Science

1. Modeling with Games

CHAPTER 1 Modeling with Games A game involves situations in which individuals are aware that their actions affect one another. To study the strategic interaction of individuals , we use game theory. Social, political, and economic interactions abound with such strategic behavior. Politics, in particular, is inherently strategic. All aspects of politics are affected by it. International relations, for example, is rife with strategic interaction, be it military or economic. Parties in a legislature or parliament regularly engage in strategic intrigue as they attempt to outmaneuver the opposition . Individual politicians must attend to strategy or their careers will be amazingly brief. Given the central role strategic interaction plays in politics, it is hardly surprising that so many have applied game theory to the study of politics. Game theoretic analysis has played a significant role in the study of political science for more than 40 years. In fact, these models have been applied to international conflict and strategic studies for almost as long as the field of game theory has existed. 1 Game theory subsequently has been employed to research in all the subfields of political science. As expected, game theoretic applications to political science have followed the same path as those of game theory in general. The intellectual history of game theory is marked by several innovations that have revolutionized the field. 2 John von Neumann derived the first prominent game theoretic I. Some of the earliest applications were seen at the RAND Corporation, where a number of prominent game theorists gathered to apply game theory to military and strategic policy. Even Pete Seeger sang about the game theorists at RAND: "The RAND Corporation 's the boon to the world / They think all day long for a fee. / They sit and play games about going up in flames / For counters they use you and me...." ("The RAND Hymn," words by Malvina Reynolds, copyright 1961 Schroder Music Co., ASCAP, renewed in 1989 by Nancy Schimmel [cited in Poundstone 1992, 83]). Some of the game theorists working at RAND in the 1940s and 19S0s included the following: John Von Neumann (the inventor of game theory), Kenneth Arrow, George Dantzig, Melvin Dreshler, Daniel Ellsberg (yes, the one of Pentagon Papers fame), R. Duncan Luce, John Nash, Anatol Rappoport, Lloyd Shapley, and Martin Shubik (Poundstone 1992, 94). 2. Readers interested in a more complete history of game theory should read Aumann (1989). 2 Games, Information, and Politics result with the Minimax Theorem in 1928.3 Game theory, however, was familiar only to mathematicians until von Neumann together with Oskar Morgenstern wrote Theory of Games and Economic Behavior (1944). All game theory applied to economics and political science can be traced back to this work. For political scientists, an equally important book in this area is Luce and Raiffa's Games and Decisions (1957). This text served as the basis for most courses on game theory at the graduate level in political science until the early 1980s (Riker 1990, 14-15). Both books prominently featured zero-sum and cooperative games. Zero-sum games model situations in which one person's gain is equal to another's loss. For example, most sports competitions are zero sum in that one player or team earns a win and the other a loss. From von Neumann and Morgenstern's discussion of zero-sum games came many features of modem game theory (such as mixed strategies), but for the most part zero-sum games have little application to political science.4 Riker notes that theoreticians at the Rand Corporation focused on zero-sum games because of their focus on the winning or losing of battles. Political scientists, however, were interested in larger events in which one actor's gains do not exactly equal the other actor's losses (Riker 1990, 15). In fact, Brams's use of zero-sum games in the The Presidential Election Game (1978) is one of the few uses of this type of game in political science. Today in political science noncooperative game theory is applied much more often than is cooperative game theory, but there was a time when cooperative game theory played a dominant role. The fundamental assumption underlying cooperative games is that binding contracts are possible; this leads to an analytical focus on how a number of players divide a joint product. The Shapley value is one of the first applications of cooperative games to politics. In fact, Shapley and Shubik (1954) was the first article to discuss game theory in a political science...