Modelling Social Dilemmas: A Regret-driven Neural Network Model

Marchiori and Warglien (2008 , Science, 319(5866), 1111–1113) showed that a simple regret-driven neural network model outperforms almost all competing models when predicting human choice behaviour in games with ‘unique equilibrium in mixed strategies’. Considering its effectiveness in this class of games, we scale up the model to account for strategically more important decision-making scenarios like prisoners’ dilemma (PD). The modification is based on the assumption that the trajectory of behaviour observed in a repeated PD experiment is the result of the bidirectional attraction between pareto-optimal (mutual cooperation) versus self-interested defection (mutual defection) in repeated PD game. The simulation results significantly capture the qualitative trends in behaviour over time.

Profit and loss sharing contracts as a prisoners dilemma: An agent based simulation with game theory application to participative finance

PLS contracts, Like Musharakah in participative finance, represent a practice of profit and loss sharing contracts. It is claimed to be a fair economic mode of investment as it entails the sharing, by the participants, of profits and risks. This mode of financing, however, suffers from asymmetric information in the form of adverse selection and moral hazards. In this Agent based simulation we managed to apply a repeated game theoretical approach to PLS financing using an agent based simulation tool called Net- logo. The purpose is to test whether PLS contracts are representative of a prisoner’s dilemma game. We have identified different parameters which are used to calculate the payoffs of the bank and the enterprise which seeks financing. Each agent in this simu- lation has some strategies that he/she can use through the game. We have managed to run the simulation1000 times for different model parameters under each combination of the agent’s strategies. We have found evidence that PLS contracts are not represen- tatives of a a prisoner dilemma game as mutual cooperation does not lead to a better payoff to the corporation than mutual defection. Over a repeated process, however, we found simulation evidence that the threat by the bank to apply an unforgiving strat- egy towards defection, leads to a cooperative behavior by the corporation through the strategy Tit-for-Tats.

Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner’s Dilemma

In the repeated prisoner's dilemma, predictions are notoriously difficult. Recently, however, Blonski, Ockenfels, and Spagnolo (2011)—henceforth, BOS—showed that experimental subjects predictably cooperate when the discount factor exceeds a particular threshold. I analyze individual strategies in four recent experiments to examine whether strategies are predictable, too. Behavior is well summarized by “Semi-Grim” strategies: cooperate after mutual cooperation, defect after mutual defection, randomize otherwise. This holds both in aggregate and individually, and it explains the BOS-threshold: Semi-Grim equilibria appear as the discount factor crosses this threshold, and then, subjects start cooperating in round 1 and switch to Semi-Grim in continuation play. (JEL C72, C73, C92, D12)

EVOLUTIONARY STRATEGY DYNAMICS FOR TAG-BASED COOPERATION AND DEFECTION IN THE SPATIAL AND ASPATIAL SNOWDRIFT GAME

Cooperation is a costly behavior undertaken by one individual which benefits another individual. Since cooperators are easily exploited by defectors (those who receive the benefits of cooperation but do not cooperate themselves), the evolution and maintenance of cooperation rely on mechanisms that allow cooperators to interact with one another more frequently than would be predicted based on their relative abundance in a population. One simple mechanism is based on the recognition of "tags" — arbitrary, yet identifiable phenotypic traits. Tags allow for the existence of conditionally cooperative strategies; e.g. individuals could adopt a strategy whereby they cooperate with tag-mates but defect against non-tag-mates. Previous research has considered the tag and strategy dynamics of unconditional and conditional strategies engaged in the Prisoner's Dilemma game, the paradigmatic framework for studying the evolutionary dynamics of cooperation, in which defection against a cooperator yields the greatest fitness payoff, followed by mutual cooperation, mutual defection, and cooperation with a defector. Here, using complementary spatial and aspatial lattice models, an alternative payoff structure is considered, based on the Snowdrift game, in which the rankings of the payoffs associated with mutual defection and cooperation with a defector are reversed relative to the Prisoner's Dilemma. In the absence of mutation, it is demonstrated that the aspatial two-tag game tends to collapse into the traditional, non-tag-based Snowdrift game, with the frequency of cooperators and defectors predicted precisely by evolutionary dynamics analysis. The spatial two-tag game, on the other hand, produces a richer variety of outcomes, whose occurrence depends on the cost-benefit ratio of mutual cooperation; these outcomes include the dominance of conditional cooperators, the dominance of unconditional defectors, and the cyclic (or noncyclic) coexistence of the two. These outcomes are then shown to be modified by mutation (which softens the transition boundaries between outcomes), and by the presence of more than two tags (which promotes nepotistic conditional cooperation).

Operant Matching as a Nash Equilibrium of an Intertemporal Game

Over the past several decades, economists, psychologists, and neuroscientists have conducted experiments in which a subject, human or animal, repeatedly chooses between alternative actions and is rewarded based on choice history. While individual choices are unpredictable, aggregate behavior typically follows Herrnstein's matching law: the average reward per choice is equal for all chosen alternatives. In general, matching behavior does not maximize the overall reward delivered to the subject, and therefore matching appears inconsistent with the principle of utility maximization. Here we show that matching can be made consistent with maximization by regarding the choices of a single subject as being made by a sequence of multiple selves—one for each instant of time. If each self is blind to the state of the world and discounts future rewards completely, then the resulting game has at least one Nash equilibrium that satisfies both Herrnstein's matching law and the unpredictability of individual choices. This equilibrium is, in general, Pareto suboptimal, and can be understood as a mutual defection of the multiple selves in an intertemporal prisoner's dilemma. The mathematical assumptions about the multiple selves should not be interpreted literally as psychological assumptions. Human and animals do remember past choices and care about future rewards. However, they may be unable to comprehend or take into account the relationship between past and future. This can be made more explicit when a mechanism that converges on the equilibrium, such as reinforcement learning, is considered. Using specific examples, we show that there exist behaviors that satisfy the matching law but are not Nash equilibria. We expect that these behaviors will not be observed experimentally in animals and humans. If this is the case, the Nash equilibrium formulation can be regarded as a refinement of Herrnstein's matching law.