The target projection dynamic

This paper studies the target projection dynamic, which is a model of myopic adjustment for population games. We put it into the standard microeconomic framework of utility maximization with control costs. We also show that it is well-behaved, since it satisfies the desirable properties: Nash stationarity, positive correlation, and existence, uniqueness, and continuity of solutions. We also show that, similarly to other well-behaved dynamics, a general result for elimination of strictly dominated strategies cannot be established. Instead we rule out survival of strictly dominated strategies in certain classes of games. We relate it to the projection dynamic, by showing that the two dynamics coincide in a subset of the strategy space. We show that strict equilibria, and evolutionarily stable strategies in $2\times2$ games are asymptotically stable under the target projection dynamic. Finally, we show that the stability results that hold under the projection dynamic for stable games, hold under the target projection dynamic too, for interior Nash equilibria.target projection dynamic; noncooperative games; adjustment

On evolutionary ray-projection dynamics

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner

Riemannian game dynamics

We study a class of evolutionary game dynamics defined by balancing a gain determined by the game's payoffs against a cost of motion that captures the difficulty with which the population moves between states. Costs of motion are represented by a Riemannian metric, i.e., a state-dependent inner product on the set of population states. The replicator dynamics and the (Euclidean) projection dynamics are the archetypal examples of the class we study. Like these representative dynamics, all Riemannian game dynamics satisfy certain basic desiderata, including positive correlation and global convergence in potential games. Moreover, when the underlying Riemannian metric satisfies a Hessian integrability condition, the resulting dynamics preserve many further properties of the replicator and projection dynamics. We examine the close connections between Hessian game dynamics and reinforcement learning in normal form games, extending and elucidating a well-known link between the replicator dynamics and exponential reinforcement learning.Comment: 47 pages, 12 figures; added figures and further simplified the derivation of the dynamic

Generalized projection dynamics in evolutionary game theory

We introduce the ray-projection dynamics in evolutionary game\ud theory by employing a ray projection of the relative �tness (vector)\ud function both locally and globally. By global (local) ray projection we\ud mean a projection of the vector (close to the unit simplex) unto the unit\ud simplex along a ray through the origin. For these dynamics, we prove\ud that every interior evolutionarily stable strategy is an asymptotically\ud stable �xed point, and that every strict equilibrium is an evolutionarily\ud stable state and an evolutionarily stable equilibrium.\ud Then, we employ these projections on a set of functions related to\ud the relative �tness function which yields a class containing e.g., best-\ud response, logit, replicator, and Brown-Von-Neumann dynamics

The target projection dynamic

We study the target projection dynamic, a model of learning in normal form games. The dynamic is given a microeconomic foundation in terms of myopic optimization under control costs due to a certain status-quo bias. We establish a number of desirable properties of the dynamic: existence, uniqueness and continuity of solution trajectories, nash stationarity, positive correlation with payoffs, and innovation. Sufficient conditions are provided under which strictly dominated strategies are wiped out. Finally, some stability results are provided for special classes of games

The Target Projection Dynamic

This paper studies the target projection dynamic, which is a model of myopic adjust-ment for population games. We put it into the standard microeconomic framework of utility maximization with control costs. We also show that it is well-behaved, since it satisfies the desirable properties: Nash stationarity, positive correlation, and existence, uniqueness, and continuity of solutions. We also show that, similarly to other well-behaved dynamics, a general result for elimination of strictly dominated strategies cannot be established. Instead we rule out survival of strictly dominated strategies in certain classes of games. We relate it to the projection dynamic, by showing that the two dynamics coincide in a subset of the strategy space. W

The target projection dynamic

We study the target projection dynamic, a model of learning in normal form games. The dynamic is given a microeconomic foundation in terms of myopic optimization under control costs due to a certain status-quo bias. We establish a number of desirable properties of the dynamic: existence, uniqueness and continuity of solution trajectories, Nash stationarity, positive correlation with payoffs, and innovation. Sufficient conditions are provided under which strictly dominated strategies are wiped out. Finally, some stability results are provided for special classes of games.

Essays on Epistemology and Evolutionary Game Theory

This thesis has two parts, one consisting of three independent papers in epistemology (Chapters 1-3) and another one consisting of a single paper in evolutionary game theory (Chapter 4): (1) “Knowing who speaks when: A note on communication, common knowledge and consensus” (together with Mark Voorneveld) We study a model of pairwise communication in a finite population of Bayesian agents. We show that, if the individuals update only according to the signal they actually hear, and they do not take into account all the hypothetical signals they could have received, a consensus is not necessarily reached. We show that a consensus is achieved for a class of protocols satisfying “information exchange”: if agent A talks to agent B infinitely often, agent B also gets infinitely many opportunities to talk back. Finally, we show that a commonly known consensus is reached in arbitrary protocols, if the communication structure is commonly known. (2) “Aggregate information, common knowledge and agreeing not to bet” I consider gambles that take place even if some – but not all – people agree to participate. I show that the bet cannot take place if it is commonly known how many individuals are willing to participate. (3) “Testing rationality on primitive knowledge” (together with Olivier Gossner) The main difficulty in testing negative introspection is the infinite cardinality of the set of propositions. We show that, under positive conditions, negative introspection holds if and only if it holds for primitive propositions, and is therefore XIV easily testable. When knowledge arises from a semantic model, we show that, further, negative introspection on primitive propositions is equivalent to partitional information structures. In this case, partitional information structures are easily testable. (4) “The target projection dynamic” (together with Mark Voorneveld) We study a model of learning in normal form games. The dynamic is given a microeconomic foundation in terms of myopic optimization under control costs due to a certain status-quo bias. We establish a number of desirable properties of the dynamic: existence, uniqueness, and continuity of solution trajectories, Nash stationarity, positive correlation with payoffs, and innovation. Sufficient conditions are provided under which strictly dominated strategies are wiped out. Finally, some stability results are provided for special classes of games