Comments on "Games with Incomplete Information Played by 'Bayesian' Players, I-III Harsanyi's Games with Incoplete Information"

The Historical Context John Harsanyi’s (1967; 1968a, b) three-part essay “Games with Incomplete Information Played by Bayesian Players” should be read today with a view to its place in the history of economic thought. It is one of the great papers that gave birth to modern information economics. Other outstanding papers in this group include William Vickrey’s (1961) paper on auctions, George Akerlof’s (1970) “Market for Lemons,” Michael Spence’s (1973) “Job Market Signaling,” and Michael Rothschild and Joseph Stiglitz’s (1976) paper on insurance markets. But Harsanyi’s contribution holds a unique place in this group of Nobel prize–winners. Each of the other papers analyzed one specific example of a market where people have different information. Harsanyi alone addressed the problem of how to define a general analytical framework for studying all competitive situations where people have different information. The unity and scope of modern information economics was found in Harsanyi’s framework. In the previous literature, as Rothschild and Stiglitz (1976) observed, economic theorists had a long tradition of banishing discussions of information to footnotes. The standard models of economic analysis assumed that all agents had the same information, and questions that went beyond the scope of these models were generally overlooked in any rigorous analysis. Even in the one great paper with a truly modern treatment of information before Harsanyi (1967; 1968a, b), Vickrey (1961) omitted any mention of informational problems from the introductory overview of his paper. Game theory was founded as an attempt to broaden the scope of economic analysis. But questions of informational structures also tended to be suppressed in the game-theory literature before 1965. This failure should be recognized as a direct consequence of the first success of game theory: the development of the normal form as a simple and general model of games. von Neumann’s (1928) first paper on game theory began by defining a general mathematical structure for modeling multistage dynamic games, called games in extensive form. These general extensive-form models allow that players may get different information during the course of a game, in which case it is called a game with imperfect information. But these extensive-form models are mathematically complex and difficult to analyze in general. So immediately after his definition of the extensive form, von Neumann (1928) argued that any multistage extensive-form game can be reduced to an equivalent one-stage game, called the normal form, where all players act simultaneously and independently. The key to this reduction is the idea of strategy. A strategy for any player in a game is defined to be a complete contingent plan of action that specifies, for every stage of the game and every possible state of the player’s information at this stage, what the player would do at this stage if he got this information. A rational player should be able to choose his entire strategy at the start of the game. The start of the game is before anybody has the opportunity to try to influence anybody else in the game, and so the players’ initial strategy choices should be independent of each other. Once all players have chosen their strategies, the expected outcome of the game becomes a matter of mechanical calculation. Thus, for any extensive-form game, von Neumann defined an equivalent one-stage game in normal form, where each player independently chooses his strategy for the given extensive-form game. The mathematical structure of the normal form consists