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Concedes instead of Fighting. Then it must be the case that u(h)(r)>(h(R). This makes sense-and Kreps and Wilson deem beliefs which satisfy this condition plausible. The key point is that one could construct "strange"equilibria in which reacting to off- equilibrium entry with F induces subsequent entrants to believe that the incumbent is Reg- ular: this could engender further entry out of equilibrium. If this is the case, the incumbent might Concede early in the game, in order to avoid ( being identified as a regular type !) You can convince yourself that the beliefs used in the construction of our "reputational luilibrium"are indeed plausible Building vs. Maintaining a Reputation Note that, in the equilibrium we have constructed, essentially nothing happens in the first ke*-1 stages. Thus, there is no sense in which the incumbent "builds a reputation"for being tough. This can only be said of the last few stages-but note that the length of the randomization phase only depends on 6, and not on the overall length of the game. Thus, one may have a very protracted play phase in which no reputation is built, and a comparatively tiny one in which actual reputation building occurs Rather, this story has to do with maintaining a reputation for toughness. Also, it should be apparent that the result depends crucially on the equilibrium assumption: consider the delicate interlocking of randomizationsConcedes instead of Fighting. Then it must be the case that µ(h)(R) ≥ µ(h 0 )(R). This makes sense—and Kreps and Wilson deem beliefs which satisfy this condition plausible. The key point is that one could construct “strange” equilibria in which reacting to off- equilibrium entry with F induces subsequent entrants to believe that the incumbent is Reg￾ular: this could engender further entry out of equilibrium. If this is the case, the incumbent might Concede early in the game, in order to avoid (!) being identified as a regular type (!!!). You can convince yourself that the beliefs used in the construction of our “reputational equilibrium” are indeed plausible. Building vs. Maintaining a Reputation Note that, in the equilibrium we have constructed, essentially nothing happens in the first k ∗ − 1 stages. Thus, there is no sense in which the incumbent “builds a reputation” for being tough. This can only be said of the last few stages—but note that the length of the randomization phase only depends on , and not on the overall length of the game. Thus, one may have a very protracted play phase in which no reputation is built, and a comparatively tiny one in which actual reputation building occurs. Rather, this story has to do with maintaining a reputation for toughness. Also, it should be apparent that the result depends crucially on the equilibrium assumption: consider the delicate interlocking of randomizations. 4
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