I present the results from a spatial model of the prisoner's dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating ($C$) or defecting ($D$). Two strategies were tested, including ``tit-for-tat'' (TFT), in which individuals play their opponent's last play, or simply playing their default play. Each individual also has a probability of telling the truth ($0 \leq P_{truth} \leq 1$) about their last play. This parameter, which can evolve over time, allows individuals to be, for instance, a defector but present as a cooperator regarding their last play. This leads to interesting dynamics where mixed populations of defectors and cooperators with $P_{truth} \geq 0.75$ move toward populations of truth-telling cooperators. Likewise, mixed populations with $P_{truth} < 0.7$ become populations of lying defectors. Both such populations are stable because they each have higher average scores than populations with intermediate values of $P_{truth}$. Applications of this model are discussed with regards to both humans and animals.

翻译：本文展示了一个在环面网格上进行的空间囚徒困境模型的研究结果。每个个体拥有默认的合作（$C$）或背叛（$D$）策略。测试了两种策略，包括“以牙还牙”（TFT）策略（个体采用对手上一轮的行动）以及直接采用默认策略。每个个体还存在一个关于其上一轮行动说真话的概率（$0 \leq P_{truth} \leq 1$）。这一可随时间演化的参数允许个体（例如）实际为背叛者，但在陈述上一轮行动时表现为合作者。由此产生了有趣的动态：当 $P_{truth} \geq 0.75$ 时，背叛者与合作者混合的群体将演化为说真话的合作者群体；而当 $P_{truth} < 0.7$ 时，混合群体将演化为说谎的背叛者群体。这两类群体均具有稳定性，因为它们的平均收益均高于具有中间 $P_{truth}$ 值的群体。本文还讨论了该模型在人类和动物行为研究中的应用前景。