Cũng lưu ý rằng ui chức năng là không nhất thiết phải lõm. Để tạo điều kiện thuận lợi cho việc phân tích tiếp theo, đó là thuận tiện để Có nhiều sự lựa chọn được thực hiện khi xây dựng một mô hình của thị trường trong đó các cá nhân gặp gỡ và đàm phán giá cả mà tại đó để thương mại. Đặc biệt, | 78 Chapter 4. The Axiomatic and Strategic Approaches which each player demands more than the maximum he can obtain at any point in S that yield the disagreement utility pair 0 0 . The Perturbed Demand Game Given that the notion of Nash equilibrium puts so few restrictions on the nature of the outcome of a Demand Game Nash considered a more discriminating notion of equilibrium which is related to Selten s 1975 perfect equilibrium . The idea is to require that an equilibrium be robust to perturbations in the structure of the game. There are many ways of formulating such a condition. We might for example consider a Nash equilibrium Ơ of a game r to be robust if every game in which the payoff functions are close to those of r has an equilibrium close to Ơ . Nash s approach is along these lines though instead of requiring robustness to all perturbations of the payoff functions Nash considered a specific class of perturbations of the payoff function tailored to the interpretation of the Demand Game. Precisely perturb the Demand Game so that there is some uncertainty in the neighborhood of the boundary of S. Suppose that if a pair of demands ơi ơ2 e S is close to the boundary of S then despite the compatibility of these demands there is a positive probability that the outcome is the disagreement point d rather than the agreement ơi Ơ2 . Specifically suppose that any pair of demands ơ1 ơ2 e Rị results in the agreement ơ1 ơ2 with probability P ơ1 ơ2 and in the disagreement event with probability 1 P ơ1 ơ2 . If ơ1 ơ2 e S then P ơ1 ơ2 0 incompatible demands cannot be realized otherwise 0 P ơ1 ơ2 1 and P ơ1 ơ2 0 for all ơ1 ơ2 in the interior of1 S. The payoff function of Player i 1 2 in the perturbed game is hi ơ1 ơ2 ơjP ơ1 ơ2 . We assume that the function P Rị 0 1 defining the probability of breakdown in the perturbed game is differentiable. We further assume that P is quasi-concave so that for each p e 0 1 the set P p ơ1 ơ2 e Rị P ơ1 ơ2 p is convex. Note that .
