The projection dynamic and the replicator dynamic

We investigate a variety of connections between the projection dynamic and the replicator dynamic. At interior population states, the standard microfoundations for the replicator dynamic can be converted into foundations for the projection dynamic by replacing imitation of opponents with “revision driven by insecurity” and direct choice of alternative strategies. Both dynamics satisfy a condition called inflow–outflow symmetry, which causes them to select against strictly dominated strategies at interior states; still, because it is discontinuous at the boundary of the state space, the projection dynamic allows strictly dominated strategies to survive in perpetuity. The two dynamics exhibit qualitatively similar behavior in strictly stable and null stable games. Finally, the projection and replicator dynamics both can be viewed as gradient systems in potential games, the latter after an appropriate transformation of the state space.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

The dynamic instability of dispersed price equilibria

We adopt an evolutionary framework to explain price dispersion as a time varying phenomenon. By developing a finite strategy analogue of the Burdett and Judd (1983) price dispersion model, we show that all dispersed price equilibria are unstable under the class of perturbed best response dynamics. Instead, numerical simulations using the logit dynamic show that price dispersion manifests itself as a limit cycle. We verify that limit cycles persist even when the finite strategy model approaches the original continuous strategy model. For a particularly simple case of the model, we prove the existence of a limit cycle.     

Can incomplete information lead to better social outcomes?

We consider a supply chain where manufacturers can be differentiated along two dimensions—product quality and cost of social responsibility effort. There are two types of manufacturers: high and low. Under complete information, high-type manufacturers exert a greater level of social responsibility effort in comparison with the low-type manufacturers. We then show that under incomplete information, high-type manufacturers have an incentive to exert an even greater level of social responsibility effort. Surprisingly, the extent of effort put in by high-type firms cannot be lower and, in some cases, can be strictly higher under incomplete information.     

The projection dynamic and the geometry of population games

The projection dynamic is an evolutionary dynamic for population games. It is derived from a model of individual choice in which agents abandon their current strategies at rates inversely proportional to the strategies' current levels of use. The dynamic admits a simple geometric definition, its rest points coincide with the Nash equilibria of the underlying game, and it converges globally to Nash equilibrium in potential games and in stable games.     

Digital Privacy: GDPR and Its Lessons for Australia

Australia's Privacy Act 1988 is under review with a view to bringing Australia's privacy laws into the digital era, more in line with the European Union's General Data Protection Regulation (GDPR). This article discusses how the GDPR can be refined and standardised to be more effective in protecting privacy in the digital era while not adversely affecting the digital economy that relies heavily on data. We argue that an ideal data policy should be informative and transparent about potential privacy costs while giving consumers a menu of opt-in choices into which they can self-select.