Schedule - Parallel Session 7 - Games and Strategic Behavior 2

IDL Boardroom - 09:00 - 10:30

Repeated games in structured populations

Matthijs van Veelen; Stefan Jagau; Julián García


We explore evolutionary dynamics in repeated games, where matching is not necessarily uniformly random, but can also be assortative. In Van Veelen et al., PNAS, 2012 we have looked at repetition and assortment, restricting attention to pure equilibria and repeated prisoners dilemma’s with “equal gains from switching”. In García & Van Veelen, JET, 2016, we have looked at repetition only, allowing for finite mixtures and prisoners dilemma’s with unequal gains from switching, but no assortment. Considering a richer set of stage games “also including coordination and anti-coordination games “and allowing for assortment gives a richer landscape of equilibria and dynamical behaviours, including cases where infinite mixtures become relevant as benchmarks, even for dynamics in finite populations.

Matthijs van Veelen

Professor, University of Amsterdam

Competitive Equilibrium in Generalized Games: A New Interpretation

Somdeb Lahiri


The purpose of this paper is to provide an alternative version of a generalized game, slightly different from the one provided in the seminal paper of Arrow and Debreu (1954). In this revised framework, we introduce the concept of a competitive equilibrium and show how it can be applied to the traditional model of general equilibrium theory. A significant result that we obtain is that a strategy profile is a competitive equilibrium if and only it is a second period maximizer of every Bergson-Samuelson social welfare function. For potential games, existence problems can be simplified. We introduce abstract economies and show that for such economies which are also potential games whose constraint correspondences all agree on the diagonal of the set of strategy profiles, existence of symmetric competitive equilibria reduces to the search for optimal solutions of dynamic choice problems. We prove existence results for the case where all the strategy sets are subsets of Euclidean spaces and for the case where all the strategy sets are non-empty and finite. The Arrow-Debreu economy is introduced in our setting as an illustration of a finite abstract economy where the preferences of the agents are independent of the strategy profile chosen in the initial period. Finally, we suggest a refinement of competitive equilibrium called an optimal competitive equilibrium and study its relationship with competitive equilibrium through some examples.

Somdeb Lahiri

Professor, PD Petroleum University

Voluntary Contributions to Real-Life Public Goods - Strategic Considerations and Contextualization

Yossi Tobol; Yuval Arbel; Ronen Bar-El; Mordechai E. Schwarz


From the early dawn of their existence, Homo sapiens have relied on voluntary contributions to their communities for gathering, hunting, planting, harvesting, establishing settlements and building religious monuments to increase their own prospects of survival (see Harari, 2014). Thus, through the evolutionary process of tens of thousands of years, contributing to achieve common goals became a “rule of thumb” for humankind (see Aumann, 1997). In this paper we address the relation between economic theory and experimental evidence. We construct a simple and tractable benchmark model examining the dynamics of contributions among individuals selfishly and strategically contributing to a public good. A unique feature of our paper is an experimental test of the theoretical model utilizing contribution game experiments to a real-life public good. We conducted four types of contribution game experiments among religious Jewish students (Orthodox and ultra-Orthodox) of the Jerusalem College of Technology (hereafter: JCT). In each of the experiments, subjects were handed an initial endowment of ECU (Experimental Currency Units) to be divided between themselves and a contribution to a real public good they value and use on a daily basis in their campus synagogues. Each participant was randomly assigned to only one of the four experiments. Experiment 1 is a five-round contribution game where contributions are dedicated to the procurement of sustainable supplies for the campus synagogue. Experiment 2 is a single-round contribution game where contributions are dedicated to the procurement of sustainable supplies for the campus synagogue. Experiment 3 is a single-round contribution game where contributions are dedicated to the ongoing operation of the campus synagogue. Experiment 4, similar to experiment 2, is a single-round contribution game where contributions are dedicated to the procurement of sustainable supplies for the campus synagogue with the difference that the participants were informed that 20% of contributions would be utilized to finance the ongoing operation of the synagogue. The results of the experiments support the model’s main theoretical predictions. We find evidence that the pattern of contributions of individuals contributing to a public good to which they attribute high intrinsic value is fairly predicted by the open-loop Nash equilibrium. In particular, we find that total contributions to the procurement of sustainable supplies increase with the time limit for collecting contributions and with group size and decrease with ongoing operating costs. We also find that average per-round contributions increase over rounds. In addition, we find evidence that individuals prefer to contribute to sustainable supplies rather than to ongoing operations, despite the assurance of contributor anonymity – that is, in real life, where contributors to buildings, facilities and the like are publicly honored, the problems of financing the ongoing operations

Yossi Tobol

Assistant Professor, Jerusalem College of Technology

The Relationship between Measures of Preferences in Public Good Games

Benjamin Beranek; Robin Cubitt; Simon Gaechter


Theory predicts under provision of public goods as the benefits of these goods are non-rivalrous and non-excludable while the individual contributions to their provision are costly. In spite of this theoretical prediction we do still observe greater contributions than expected in both real-world situations as well as in laboratory experiments. It further appears that contribution behavior follows distinct patterns such as conditional cooperation in which people match contributions they believe others will contribute and free riding in which people never contribute to the public good (Fischbacher, Gächter, & Fehr, 2001) [FGF]. Many possible behavioral motivations have been offered to explain these patterns of behavior. In this study our primary aim is to see if inequality aversion can explain these FGF patterns of conditional cooperation. Further, our research design allows us to examine (a) the association between FGF types and direct response public good game contributions (providing a robustness check to the results of Fischbacher, Gächter, & Quercia, 2012) as well as (b) the association between inequality aversion parameters, beliefs, and direct response public good game contributions (replicating the results of Blanco, Engelmann, & Normann, 2011 with greater specificity). Using a within subject design, we employ the Blanco, Engelmann, & Normann, 2011 method to parametrize inequality aversion using the modified dictator game and the FGF public good game with contribution table to observe contribution behavior patterns. We compare these measures one to another to answer our primary research question of whether inequality aversion can explain the FGF patterns of conditional cooperation. We further use the results of these games to make inequality aversion predictions and FGF predictions for a separate direct response public good game. We observe that distributions of β values (the parameter of advantageous inequality aversion) vary by FGF type with conditional cooperators having higher β values than free riders. We also observe that most people tend to contribute the amount predicted by theory or deviate by contributing even more, rather than less, than the amount expected. These results show that, while it can account for some public goods provision, inequality aversion is likely to be just one of many behavioral motivations at play in the public goods contribution decision making process. In a final exercise to evaluate these two behavioral motivations one against another, we conduct a horse race between these two competing explanations of public good game contributions: parameter based inequality aversion predictions and the strategy based FGF predictions.

Benjamin Beranek

PhD Student, University of Nottingham