Reciprocation Effort Games
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Abstract
Consider people dividing their time and eort between friends, interest clubs, and reading seminars. These are all reciprocal
interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on ecient eort division, we determine the existence and eciency of the Nash equilibria of the game of allocating eort to such projects. When no minimum eort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal eort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model,
assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.