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

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

On the computation of large sets of rewards in ETP-ESP-games with communicating states

Games with endogenous transition probabilities and endogenous stage payoffs (or ETP-ESP-games) are stochastic games in which both the transition probabilities and the payo¤s at any stage are continuous functions of the relative frequencies of all action combinations chosen in the past. We present methods to compute large sets of jointly-convergent pure-strategy rewards in ETP-ESP-games with communicating states. Such sets are useful in determining feasible rewards in a game. They are also instrumental in obtaining the set of (Nash) equilibrium rewards

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

2010,24: 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 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

2011,09: 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 "subjective" games in the class of social dilemmas. Which unique "subjective" game is actually played depends crucially on how the agents discount their future payoffs. We examine equilibrium behavior and its consequences on sustainability of the common-pool resource system under exponential and hyperbolic discounting. A suffcient 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 suffciently 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

A Note on Repeated Games with Vanishing Actions

A two-person general-sum repeated game with vanishing actions is an infinitely repeated game where the players face the following restrictions. Each action must be used by player k ¿ {1,2} at least once in every rk ¿ ¿ consecutive stages, otherwise the action vanishes for the remaining play. We assume that the players wish to maximize their limiting average rewards over the entire time-horizon.A strategy-pair is jointly convergent if for each action pair a number exists to which the relative frequency with which this action pair is chosen, converges with probability one. A pair of feasible rewards is called individually rational if each player receives at least the threat-point reward, i.e., the amount which he can guarantee himself regardless of what the opponent does given r1, r2 and the actions available in the long run. In a repeated game with vanishing actions, there may exist multiple threat points which are endogenous to the play.We prove that all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Furthermore, each convex combination of individually-rational jointly-convergent pure-strategy rewards, can be supported by an equilibrium for m × n-games provided r1 > m ¿ 2, r2 > n ¿ 2. Keywords: Stochastic games; vanishing actions; limiting Average rewards; endogenous threat