Strategic Behavior in Contests: Reply
作者回应Baye和Shin对其1987年论文的评论，指出对称竞赛中承诺策略的一阶效应为零，但非对称情形下存在一阶收益，并认为后者更具经济意义。
In my 1987 paper, I modeled contests where the probability of each player winning a prize depends on all players’ efforts, and examined the first-order benefits to one player of making a commitment to a strategy slightly different from his Nash equilibrium strategy. In the special case of a two-player symmetric contest, I found that this first-order effect was zero. Michael R. Baye and Onsong Shin (1999) have taken the useful further step of finding the second-order conditions which ensure that the local stationary point is a local maximum. They also find an example where such a commitment has a third-order benefit. Whether this is of any substantive economic interest remains to be seen. I used the phrase “no local effect” to mean zero first-order effect, which was clearly a sloppy use of language. But some such restriction on the use of “local” is essential. If the phrase “x has no local effect on f (x) at x 5 a” were to mean that all derivatives f (a) are zero, then a Taylor series expansion would show that f (x) 5 f (a) for all x, and “no local effect” would be the same as “no global effect.” Most importantly, symmetric contests were only a very special case of my model. The focus was on the much more interesting and more general situation of asymmetry among the players, where one player’s commitment to a strategy different from his Nash equilibrium strategy does bring him a first-order benefit— the favorite benefits by committing to excessive effort, and the underdog from committing to too little. Others, for example, Kyung H. Baik and Jason F. Shogren (1992), have extended the analysis to endogenize the order of moves and found that it can be in the interests of both contestants to let the underdog make the commitment. In my view these are the more interesting economic issues to do with contests than are third-order effects in the symmetric case.