Equilibrium in a modification of VCG mechanism (efficiency instead of dominant strategies)

<p>This paper deals with a modification of the Vickrey-Clark-Groves mechanism. While being perfectly efficient and strategy proof, the VCG mechanism suffers from what is known as unbalanced budget. That means that, to run a mechanism, a certain amount of money has to be wasted. In the paper we propose to amend the mechanism by dividing equally among the participants of the VCG mechanism the surplus to be wasted. Although such amendment makes the mechanism not strategy-proof, it helps to balance the budget. In the paper equilibrium strategies of players are calculated, second order conditions are examined and constraints on the initial conditions are derived. For some particular cases convergence of players&rsquo; strategies is analyzed. &nbsp;It has been shown that in the case of one item to bid for there exists one equilibrium, which converges evenly to the function y(x)=x (an equilibrium in the conventional Vickrey-Clark-Groves mechanisms) when the number of players increases, and continuum of equilibria in which convergence does not performed. In the case of two items to bid for a continuum of equilibria exists where strategies diverges and one equilibrium that does not go to infinity with the growth of the number of participants.</p>