STRATEGY-PROOF AND EFFICIENT EXCHANGE ON A FINITE SET OF COBB-DOUGLAS UTILITY FUNCTIONS

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We consider the possibility of designing strategy-proof and efficient social choice functions in two-agent, two-good, pure exchange economies. First, we show the nonexistence of strategy-proof, efficient, and symmetric social choice functions on an arbitrary domain with the following three Cobb-Douglas utility functions: (I) u_α(x_A, x_B) = (x_A)^2/3(x_B)^1/3, (ii) u_β(x_A, x_B) = (x_A)^1/2(x_B)^1/2, and (iii) u_γ(x_A, x_B) = (x_A)^1/3(x_B)^2/3,. Second, we conjecture that any strategy-proof and efficient social choice function is dictatorial on an arbitrary subset of Cobb- Douglas utility functions with the above (I)-(iii).

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