Summary: It is the purpose of the paper to analyze a bargaining situation with the help of the equilibrium selection theory of J. C. Harsanyi and R. Selten. This theory selects one equilibrium point in every finite non-cooperative game.
The bargaining problem is the following one: the two bargainers - player 1 and player 2 - simultaneously and independently propose a payoff x of player 1 in the interval \(<0,1>\). If agreement is reached player 2’s payoff is 1-x. Otherwise both receive zero.
Each player i has a further alternative \(W_ i\), namely not to bargain at all \((i=1,2)\). Thereby he avoids transaction costs c and d of bargaining which arise whether an agreement is reached or not. One may think of an illegal deal where bargaining involves a risk of being punished - independently whether the deal is made or not.
The model has the form of a \((K+1)\times (K+1)\)-bimatrix game. It is assumed that there is an indivisable smallest money unit. The game has \(K+1\) pure strategy equilibrium points. K of them correspond to an agreement and the last one is the strategy pair where both players refuse to bargain. Each of the \(K+1\) equilibrium points can be the solution of the game. The aim of the Harsanyi-Selten-theory is to select in a unique way one of these equilibrium points by an iterative process of elimination (by payoff dominance and risk dominance relationships) and substitution. For each parameter combination (c,d) a sequence of candidate sets arises which becomes smaller and smaller until finally a candidate set with exactly one equilibrium point - the solution of the game - is found.