Bargaining theory and rational threats

A further issue in bargaining is the source or interpretation of the disagreement point D, the point which the parties would fall back on if they fail to agree. In the context of law and economics, failing to reach agreement usually means going to trial. Each party's likelihood of success in court therefore determines the position of their disagreement point. In other words, in law and economics, the disagreement point is rarely fixed and exogenous.

To analyse this situation, Nash (1951) formulated the concept of rational threats. The basic idea of rational threats is as follows. Consider a situation where the disagreement point is variable, and can be influenced by the parties before they enter negotiations. That is, there are now two stages to the bargaining process:

  • • Stage 1: The parties engage in activities which influence their own disagreement point as well as that of their opponents.
  • • Stage 2: The parties begin from the disagreement points that emerge from stage 1, and bargain and reach an agreement according to the Nash solution.

To analyse this game, we need to first write down the payoffs and be explicit about the strategies of the parties. We will use the factory and the residents example again. Let the strategies in the first stage of the game be denoted by (sF, sR). The disagreement points of the factory is dF (sF, sR), and the disagreement point of the residents is dR(sF, sR). The payoffs in the final stage of the game are:


This is called a rational threat game. The model can be solved by simply finding the Nash equilibrium (s*, s*) of the game in which the players have the payoffs in (11.12) and (11.13). This is a very natural way of modelling legal disputes in a more realistic setting, where players can employ lawyers and gather evidence before trial in order to influence their threat points at the negotiating table, and in doing so, make themselves better off.

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