Faculty of Science, University of South Bohemia, Branišovská 1760, 370 05 České Budějovice, Czech Republic; Institute of Entomology, Biology Centre, Czech Academy of Sciences, Branišovská 31, 370 05 České Budějovice, Czech Republic.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada.
J Theor Biol. 2022 Aug 21;547:111162. doi: 10.1016/j.jtbi.2022.111162. Epub 2022 May 14.
The classic Hawk-Dove game is a symmetric game in that it does not distinguish between the winners and losers of Hawk-Hawk or Dove-Dove contests. Either of the two interacting Hawks or the two interacting Doves have the same probability to win/lose the contest. In addition, all pairwise interactions take the same time and after disbanding, the individuals pair instantaneously again. This article develops an asymmetric version of the Hawk-Dove model where all costs are measured by the time lost. These times are strategy dependent and measure the length of the conflict and, when a fight occurs between two interacting Hawks, the time an individual needs to recover and pair again. These recovery times depend on whether the Hawk won or lost the contest so that we consider an asymmetric Hawk-Dove game where we distinguish between winners and losers. However, the payoff matrix for this game does not correspond to the standard bimatrix game, because some entries are undefined. To calculate strategy payoffs we consider not only costs and benefits obtained from pairwise contests but also costs when individuals are disbanded. Depending on the interacting and recovery times, the evolutionary outcomes are: Hawk only, both Hawk and Dove, and a mixed strategy. This shows that measuring the cost in time lost leads to a new prediction since, in the classic (symmetric) Hawk-Dove model that does assume positive cost (C>0), both Hawk and Dove strategy is never an evolutionary outcome.
经典的鹰鸽博弈是一个对称博弈，因为它没有区分鹰鹰或鸽鸽比赛的赢家和输家。两种相互作用的鹰或两种相互作用的鸽都有相同的概率赢得/输掉比赛。此外，所有的两两相互作用都需要相同的时间，并且在解散后，个体立即再次配对。本文开发了一个不对称的鹰鸽模型版本，其中所有的成本都用失去的时间来衡量。这些时间是策略相关的，衡量冲突的长度，当两个相互作用的鹰发生冲突时，个体需要恢复和再次配对的时间。这些恢复时间取决于鹰是否赢得比赛，因此我们考虑一个区分赢家和输家的不对称鹰鸽博弈。然而，这个游戏的收益矩阵并不对应于标准的双矩阵游戏，因为有些条目是未定义的。为了计算策略收益，我们不仅考虑了从两两比赛中获得的成本和收益，还考虑了个体解散时的成本。根据相互作用和恢复时间，进化结果是：只有鹰、鹰和鸽、以及混合策略。这表明，用失去的时间来衡量成本会产生一个新的预测，因为在经典的（对称的）鹰鸽模型中，假设存在正成本（C>0），鹰和鸽策略都不是进化的结果。
