4. Discussion and Conclusion
We have shown that variants of the Shapley-Shubik market game model with production can generate an equilibration mechanism that can lead to multiple equilibria when the number of active firms is small. The equilibration process can accommodate nominal price rigidities, without any need for enforcing menu costs or other additional restraints on price adjustment. We also explicitly show the relationship between a typical firm’s markup of price over marginal cost and its market share. The model itself is silent on what might cause price rigidities, and how different mechanisms (e.g., menu costs, search frictions, and learning) might interact with the basic model. We believe there are some interesting arguments in favor of learning and evolutionary dynamics that arise from the general equilibrium considerations in our analysis.
The problems with finding effective mechanisms for implementing equilibrium prices in competitive economies are well known. Scarf (1960)’s example shows that the presence of strong income effects can make simple price adjustment dynamics like the Walrasian tatonnement process ineffective. While the market game does provide an explicit price formation mechanism via the ratio of expenditure flows to quantity flows, Kumar and Shubik (2004) show that the market game is not immune to Scarf (1960)-like problems for simple adjustment dynamics akin to tatonnement.
