Exchange Markets: Strategy meets Supply-Awareness

Market equilibrium theory assumes that agents are truthful, and are generally unaware of the total supply of goods in the market. In this paper, we study linear exchange markets with each of these assumptions dropped separately, and show a surprising connection between their solutions. We define the exchange market game as where agents strategize on their utility functions, and we derive a complete characterization of its symmetric Nash equilibria (SNE). Using this characterization we show that the payoffs at SNE are Pareto-optimal, the SNE set is connected, and we also obtain necessary and sufficient conditions for its uniqueness. Next we consider markets with supply-aware agents, and show that the set of competitive equilibria (CE) of such a market is equivalent to the set of SNE of the corresponding exchange market game. Through this equivalence, we obtain both the welfare theorems, and connectedness and uniqueness conditions of CE for the supply-aware markets. Finally, we extend the connection between CE and SNE to exchange markets with arbitrary concave utility functions, by restricting strategies of the agents to linear functions in the game, and as a consequence obtain both the welfare theorems.