Four Contributions to Experimental Economics

In the following four chapters, distinct but related experimental research analyzing strategic and non-strategic economic behavior is presented. Chapter 2, entitled "Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games" is a systematic study of behavior in symmetric and asymmetric prisoner's dilemma games. The prisoner's dilemma is one of the key models in many disciplines for now over five decades. Previous prisoner's dilemma experiments show that in contrast to theoretical predictions, cooperation rates are generally very high in the symmetric payoff variant of the game. Chapter 2 studies cooperation in the prisoner's dilemma in a more realistic scenario by systematically analyzing the effects of asymmetric payoffs. Already in the early nineties Murnighan et al. (1990) noted that "research has been inexplicably absent on the effects of asymmetry". The present study takes this concern into account and focuses on this much broader type of conflict expanding the limited and rather unsystematic research conducted in this area. It analyzes and discusses the effect of asymmetry on cooperation in a 40 period prisoner's dilemma game in fixed partner design. A distinction is made between a high and low payoff symmetric prisoner's dilemma on the one hand and an asymmetric game combined out of both symmetric ones on the other hand. Asymmetry significantly decreases cooperation, as low-type players are more likely to defect after mutual cooperation while high-type players initiate cooperation more often than the former. Asymmetry also has a significant negative effect on the stability of cooperation rendering long sequences of mutual cooperation extremely rare. These results are not only a valuable addition to the existing (mostly symmetric) prisoner's dilemma literature but are also of relevance for understanding reciprocity, equity and fairness especially in light of recent theoretical developments based exclusively on symmetric experimental games. Chapter 3, entitled "Assignment versus Choice in Prisoner's Dilemma Experiments'' compares behavior in a repeated prisoner's dilemma game when players can choose between two different representations of the same prisoner's dilemma, to behavior when players are assigned to play a specific game. The chapter is concerned with the methodological question of the external validity of experimental research based on the assignment of participants to experimental games or decision situations. Experimental findings may systematically misrepresent field outcomes if assigning participants to experiments has an impact on the decisions made by the participants in the experiment and if such an assignment does not occur in the field. The chapter therefore analyzes to what extent experimental deviations from actual situations due to the assignment of participants is based exclusively on the possibility of self-selection or sorting, or whether choice has an important behavioral effect in itself. The chapter extends the results obtained in the experimental psychology literature by analyzing whether choice effects are also found in strategic contexts, rendering them of particular interest to economic environments. Based on the idea that choice either via active modification of the strategic environment or by passive self-selection into a particular strategic environment may be an important property of many empirical problems studied using experimental methods, the research goal is to separate a choice effect from sorting or self-selection effects. The experimental results clearly indicate that the mere fact that participants can choose the game they want to play has a statistically significant impact on behavior. Cooperation rates are up to 60% higher in the games that were not assigned to but chosen by participants. These findings are consistent with the robust evidence of the psychology literature on non-strategic contexts that choice increases motivation, trust, and performance. Given that in many contexts agents choose the strategic situation they get involved in, assigning participants to experiments may affect the external validity of some experimental findings. Chapter 4, entitled "The Role of Rivalry - Public Goods versus Common-Pool Resources" moves from the 2 person prisoner's dilemma game structure to the analysis of behavior in a 4 person quadratic public good and a quadratic common-pool resource game. Despite a large theoretical and empirical literature on public goods and common-pool resources, a systematic comparison of these two types of social dilemmas is lacking. In fact, there is some confusion about these two types of dilemma situations. As a result, they are often treated alike. An explicit example of this is provided by Gintis (2000) who argues that while "common pool resource and public goods games are equivalent for Homo Oeconomicus, people treat them quite differently in practice. This is because the status quo in the public goods game is the individual keeping all the money in the private account, while the status quo in the common pool resource game is that the resource is not being used at all." In line with the theoretical literature, the chapter first establishes theoretically that public good and common-pool resource games as used in the experimental literature are two distinct types of social dilemmas, the fundamental difference between the two games being the degree of rivalry. It is shown that the distinguishing feature of these two types of games lies in the distributional factor that determines whether the good is rival or non-rival. This difference gives rise to two distinct strategic environments. Based on these theoretical differences an experiment is devised that tests whether the theoretical differences have an impact on behavior. The results show that participants clearly respond to the differences in rivalry. Aggregate behavior in both games starts relatively close to Pareto efficiency and converges quickly to the respective Nash equilibrium. This clearly indicates that the differences in rivalry affect behavior, strengthening the importance of differentiating between the two types of games. Despite this difference reflecting the structure of the two games, there appear to be some behavioral similarities. In both games, aggregate behavior starts in the neighborhood of the Pareto optimum and moves rather quickly to the respective aggregate Nash equilibrium. Chapter 5 entitled "Purchase Decisions with Non-linear Pricing Options under Risk" moves away from a strategic game setting to an analysis of decisions under risk. The chapter reports on an experimental investigation of purchase decisions with linear and non-linear pricing under risk. Standard economic theory suggests that customers should be indifferent to the format of a price reduction. In particular this implies that one would expect a customer to switch from one pricing scheme to another (one supplier to another) as long as there is at least an expected reduction in the effective purchase price. The recent surge in the use of rebates, discounts, bonus and point schemes implemented by retailers but also observed in other levels of the production chain begs the question of whether traditional economic explanations do fully account for the increased usage of non-linear pricing methods. An understanding of potential behavioral reasons for using such pricing schemes - as presented in this chapter - may not only be relevant for their design, but also for wider policy considerations. The experiment presented is based on a single period stochastic inventory problem with endogenous cost. It extends classic binary lottery experiments to test standard decision theoretic predictions concerning purchasing behavior in a rebate and a discount scheme. The question to what extent customers continue to purchase under two mathematically isomorph formats of non-linear schemes even if switching to a linear pricing scheme is optimal is investigated. The results indicate that rebate and discount schemes exert a statistically significant attraction on customers. Given the increased role of non-linear pricing schemes, systematic deviations from optimal behavior are an important element in the design of such schemes and may raise consumer protection and competition policy issues. The chapter concludes with a discussion on how the results can be explained by decision heuristics.</p

Open-ended Learning in Symmetric Zero-sum Games

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective -- we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield open-ended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response, PSRO_rN) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply PSRO_rN to two highly nontransitive resource allocation games and find that PSRO_rN consistently outperforms the existing alternatives.Comment: ICML 2019, final versio

On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual convergence of fixpoint computations. In particular, we are able to directly obtain several new decidability results on lossy channel systems.Comment: 16 page

Statistical Mechanics of Dilute Batch Minority Games with Random External Information

We study the dynamics and statics of a dilute batch minority game with random external information. We focus on the case in which the number of connections per agent is infinite in the thermodynamic limit. The dynamical scenario of ergodicity breaking in this model is different from the phase transition in the standard minority game and is characterised by the onset of long-term memory at finite integrated response. We demonstrate that finite memory appears at the AT-line obtained from the corresponding replica calculation, and compare the behaviour of the dilute model with the minority game with market impact correction, which is known to exhibit similar features.Comment: 22 pages, 6 figures, text modified, references updated and added, figure added, typos correcte

Best Responding to What? A Behavioral Approach to One Shot Play in 2x2 Games

We introduce a simple procedure to be used for selecting the strategies most likely to be played by inexperienced agents who interact in one shot 2x2 games. We start with an axiomatic description of a function that may capture players' beliefs. Various proposals connected with the concept of mixed strategy Nash equilibrium do not match this description. On the other hand minimax regret obeys all the axioms. Therefore we use minimax regret to approximate players' beliefs and we let players best respond to these conjectured beliefs. When compared with existing experimental evidences about one shot matching pennies games, this procedure correctly indicates the choices of the vast majority of the players. Applications to other classes of games are also explored

Interdependent security experiments

This paper analyzes the behavior of subjects in interdependent security experiments which exhibit strategic complementarity. In these experiments, subjects decide whether to pay to mitigate the risk of a loss, but the exact risk depends on the actions of other subjects. Two ranked equilibria exist, and the efficient equilibrium is for all agents to pay for the mitigation. Subjects in the interdependent security experiments rarely coordinate on the efficient equilibrium. Coordination is slightly more common in similar coordination games without the risk mitigation decision. The experiments also compare the effectiveness of two policies at inducing higher levels of mitigation.experiments, coordination game, risk mitigation, interdependent security

Random replicators with asymmetric couplings

Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically to address cases with asymmetric interactions where there is no Lyapunov function governing the dynamics. We here focus on replicator models with Gaussian couplings of general symmetry between p>=2 species, and discuss how an effective description of the dynamics can be derived in terms of a single-species process. Upon making a fixed point ansatz persistent order parameters in the ergodic stationary states can be extracted from this process, and different types of phase transitions can be identified and related to each other. We discuss the effects of asymmetry in the couplings on the order parameters and the phase behaviour for p=2 and p=3. Numerical simulations verify our theory. For the case of cubic interactions numerical experiments indicate regimes in which only a finite number of species survives, even when the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of negatively correlated couplings added, figures adde