The Matching And The Moral Hazard

 

Norovsambuu Tumennasan

 

   We study the matching problem when the actions of the players are not verifiable and the size of possible matching is not greater r. Once the players are matched they engage in a risky public project by exerting the efforts, which cannot be contracted upon. By assuming that the players anticipate Nash equilibrium outcomes from all coalitions, any player's payoff from a coalition containing her is completely defined by her and other members' preferences. By further assuming that players' utility functions are the sum of utility from a public good, which is dependent on productivity weighted sum, and quadratic disutility function from one's effort, we show several existence results on a stable r-matching. These results hinge on
the shape of discount function which is a credit given for a successful project and it depends on the size of a coalition. If it is constant, then a stable r-matching exists. If it is non-increasing then a stable r-matching exists if the quota for matching is not greater than 3. Furthermore, the algorithm which yields a stable r-matching is given and this algorithm matches the players assortatively by coefficients of attractiveness which is a
combination of marginal cost, productivity and value for a successful project. Finally, we study the statics of stable r-matching.