Competition form of bargaining

We consider the noncooperative zero-sum game, related with the competitions. Players submit the competition projects, that are characterized by a finite set of parameters. The arbitrator or arbitration committee uses a stochastic procedure with the probability distribution to determine the most preferred project. This distribution is known to all participants. Payoff ot the winner depend on the parameters of his project. The three-dimensional mathematical model of this problem is constructed, which is then extended to the multi-dimensional case. The equilibria in the games with four and $n$ persons are found, as well as the corresponding payoffs are computed.