A BAYESIAN GAME FOR A PROFIT AND LOSS SHARING CONTRACT

Abstract

This paper presents a Bayesian game model for a profit-and-loss sharing (PLS) contract. We develop the model in two parts, one for a non-social bank and the other for a social bank. The model is proposed to reduce the adverse selection problem inherent in PLS contracts. The game starts with incomplete information; Islamic banks do not know exactly what type of agent is applying for a PLS contract, and whether the agents are efficient or non-efficient. We assume that the banks assign the agent type to a prior probability. Determination of the profit-sharing ratio of the contract is then discussed, and we look for the Bayesian Nash equilibrium as a solution or outcome of the game. We show that banks offer interesting but risky contracts to agents if they assign high probability to the agents being efficient.  In contrast, they offer less risky contracts if they assign high probability to the agents being non-efficient. The results can be considered by Islamic banks to reduce the adverse selection problem in PLS contracts.