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UBC Theses and Dissertations

Economic resource allocation under uncertainty and differential information - a unified game approach with agency and accounting applications Amershi, Aminmohamed Hassanali


The central economic problem is the allocation of resources in groups in an environment with uncertainty, externalities and differential information. Given that a group of interacting agents may have different preferences and beliefs, different abilities and decision choices, and differential information about the environment, the issue is the group choice of contracts which determine joint strategies, information systems and rules to share jointly produced wealth. A number of accounting paradigms such as transfer pricing, divisional cost allocation, equity accounting, partnership accounting, budgetary control mechanisms and the like can be cast into this framework. This study develops a general game (i.e., games without side payments) model which provides a unified treatment of the resource allocation problem. The basic mathematical theory used is the theory of general games as developed by Aumann, Peleg, Bondareva, Scarf and Shapley among others. The fundamental result used is an equilibrium existence result for weak core solutions of general games by Scarf [1967]. We extend the scope of Scarf's existence result to group choice of contracts determining the choice of action strategies, information systems and wealth sharing rules in an uncertain environment with informational asymmetries (differential information). Again, the existence results for the general problem are used to derive additional marginalist insights into the agency problem. Interpretation of the general results in an accounting information systems framework provides insights into accounting issues. The complexity of the problem necessitates the use of technical mathematical material from probability and measure theory and mathematical programming in function space. The first conclusion of the study is that the general game or negotiation mechanism can successfully model the bargaining process by which groups arrive at agreements on Pareto-optimal contracts which determine joint strategies, information systems (both for strategy choice and performance evaluation) and wealth-sharing rules. This is proved by the existence of a particular type of equilibrium, namely the Pareto- optimal weak core contracts, in very general situations involving uncertainty and differential information. A second conclusion is that the formulation can incorporate as special cases - syndicate risk-sharing, agency theory,etc. - to be termed a meta model. Using the existence results, we conclude, for instance, that the problem of assigning weights to the utilities of the agents in syndicate and risk-sharing theory can be resolved. The third conclusion is that the negotiation mechanism is posterior efficient in the sense that negotiated contracts are enforceable by the use of penalty schemes. Since the mechanism is also prior efficient (i.e., it can produce Pareto-optimal weak core contracts), we conclude that the game mechanism is efficient. Specialising the general results to the agency problem, we conclude that in an agency with homogeneous beliefs, the agent's desired wage rate is revealed by his marginal productivity. Also, it is possible to derive general equalities relating marginal utilities of the principal and agent which, result from necessary Lagrangean conditions for a prior and posterior efficient agency. The interpretation of the general weak-core existence result under differential information allows us to conclude in the context of accounting systems that the principle of disclosure is conducive to the proper functioning of the negotiation mechanism. Again, the interpretation of the posterior efficiency results allows us to conclude that negotiated feedback control mechanisms such as budgetary control systems are possible in fairly general situations.

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