Non-Cooperative Bargaining with Unsophisticated Agents

A traditional non-cooperative bargaining situation involves two or more forward-looking players making offers and counteroffers alternately until an agreement is reached, with a penalty according to the time taken by players in the decision-making process. We introduce a game that aids myopic players to reach the equilibrium as if they were forward-looking agents. The key elements of the game are that players are penalized both for their deviation from the previous best-reply strategy and their time taken for the decision-making at each step of the game. It is shown that our game has an equilibrium not only for the traditional processes and utilities used in traditional non-cooperative bargaining literature, but for an expanded and very comprehensive set of stochastic processes (such as Markov processes) and utility functions. Our work not only complements traditional non-cooperative bargaining literature for myopic agents, but also enlarges the class of processes and functions where Rubinstein's non-cooperative bargaining solutions might be defined and applied.