Thermodynamics of evolutionary games.
Thermodynamics of evolutionary games.
复制标题
进化博弈的热力学。
作者：
C. Adami;A. Hintze
玩家之间的合作如何进化是生物学中尚未解决的问题。在这里，我们使用伊辛型模型的哈密顿动力学来描述合作和背叛参与者的总体，以表明合作者的平衡分数由类似于磁化的热观察值的期望值给出。我们将这种形式主义应用到三个参与者的公共物品博弈中，并证明了合作与背叛之间的相变，相当于一维伊辛晶体中具有远程相互作用的相变。然后，我们调查了惩罚对合作的影响，发现惩罚扮演了一个磁场的角色，导致玩家之间的“结盟”，从而鼓励合作。我们认为，通过挖掘低维自旋系统中丰富的临界动力学文献，合作进化的热哈密顿图可以产生关于进化群体动力学的其他见解。
How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the public goods game with three players and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an "alignment" between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems.