Social dilemmas, time preferences and technology adoption in a commons problem

Agents interacting on a body of water choose between technologies to catch fish. One is harmless to the resource, as it allows full recovery; the other yields high immediate catches, but low(er) future catches. Strategic interaction in one 'objective'resource game may induce several 'subjective' games in the class of social dilemmas. Which unique 'subjective'game is actually played depends crucially on how the agents discount their future payo¤s. We examine equilibrium behavior and its consequences on sustainability of the common-pool resource system under exponential and hyperbolic discounting. A sufficient degree of patience on behalf of the agents may lead to equilibrium behavior averting exhaustion of the resource, though full restraint (both agents choosing the ecologically or environmentally sound technology) is not necessarily achieved. Furthermore, if the degree of patience between agents is sufficiently dissimilar, the more patient is exploited by the less patient one in equilibrium. We demonstrate the generalizability of our approach developed throughout the paper. We provide recommendations to reduce the enormous complexity surrounding the general cases

Attractive evolutionary equilibria

We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain evolutionary dynamics. For instance, each attractive evolutionarily stable strategy is an attractive evolutionarily stable equilibrium for certain barycentric ray-projection dynamics, and vice versa

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

Strong and Weak Rarity Value: Resource Games with Complex Price–Scarcity Relationships

We analyze effects of rarity value on the sustainability of a natural resource. Rarity value means that under extreme scarcity of the resource unit profits increase ‘explosively.’ We focus on equilibrium behavior of very patient agents in a Small Fish War. Agents interacting on a body of water have two options: they can fish with restraint or without. Fishing with restraint allows the fish stock to recover; fishing without yields higher immediate but lower future catches. We distinguish weak and strong rarity value; for the strong (weak) variant, total symmetric Pareto-efficient rewards are higher (lower) than those obtained by keeping the price fixed at highest-resource-stock level. Only for strong rarity value, the price effect more than compensates for smaller sustainable catches. Pareto-efficient equilibrium behavior dictates that lowest sustainable stocks are targete

Long-run strategic advertising and short-run Bertrand competition

We model and analyze strategic interaction over time in a duopoly. Each period the firms independently and simultaneously take two sequential decisions. First, they decide whether or not to advertise, then they set prices for goods which are imperfect substitutes. Not only the own, but also the other firm's past advertisement e¤orts a¤ect the current "sales potential" of each firm. How much of this potential materializes as immediate sales, depends on current advertisement decisions. If both firms advertise, "sales potential" turns into demand, otherwise part of it "evaporates" and does not materialize. We determine feasible rewards and (subgame perfect) equilibria for the limiting average reward criterion. Uniqueness of equilibrium is by no means guaranteed, but Pareto efficiency may serve very well as a refinement criterion for wide ranges of the advertisement costs

Strong and weak rarity value in Small Fish Wars

We analyze the effects of rarity value on the economic and ecological sustainability of a natural resource. Rarity value means that under extreme scarcity of the resource unit profits increase 'explosively'. We focus on equilibrium behavior of very patient agents in a Small Fish War. In such a setting, agents interacting on a body of water have two options: they can fish with restraint or without. Fishing with restraint allows the fish stock to recover; fishing without yields higher immediate but lower future catches. We make a distinction between weak and strong rarity value. In the weak variant, equilibrium behavior induces high sustainable fish stocks and long-run yields. In the strong one, very high equilibrium rewards may be obtained by almost exhausting the resource, but more moderate equilibrium rewards are feasible without endangering sustainability

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

Stochastic games with endogenous transitions

We introduce a stochastic game in which transition probabilities depend on the history of the play, i.e., the players' past action choices. To solve this new type of game under the limiting average reward criterion, we determine the set of jointly-convergent pure-strategy rewards which can be supported by equilibria involving threats. We examine the following setting for motivational and expository purposes. Each period, two agents exploiting a fishery choose between catching with restraint or without. The fish stock is in either of two\ud states, High or Low, and in the latter each action pair yields lower payoffs. Restraint is harmless to the fish, but it is a dominated strategy in each stage game. Absence of restraint damages the resource, i.e., the less restraint the agents show, the higher the probablities that Low occurs at the next stage of the play. This state may even become 'absorbing', i.e., transitions to High become impossible