Ambiguity when playing coordination games across cultures

Cultural differences can be a source of ambiguity in coordination games. As players are likely to experience more ambiguity when playing a different culture, we expect players to choose safer strategies. We run experiments with a stag hunt and bargaining coordination game. Using a between-subjects design, we vary the identity of the opponent between someone of the same culture or a different culture. We compare the responses of British and East Asian students at the University of Exeter and show the cultural identity of the opponent by physical appearance. While we find no significant differences between treatments for East Asians, the British choose the safer option in the stag hunt and demand more of the pie in the bargaining game when faced with an opponent from a different culture.

     

Nash Equilibrium with Lower Probabilities

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings.     

Coalitional Interval Games for Strategic Games in Which Players Cooperate

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, studies, and characterizes a natural method of associating coalitional interval games with strategic games.      

Strategic ambiguity and decision-making: an experimental study

We conducted a set of experiments to compare the effect of ambiguity in single-person decisions and games. Our results suggest that ambiguity has a bigger impact in games than in ball and urn problems. We find that ambiguity has the opposite effect in games of strategic substitutes and complements. This confirms a theoretical prediction made by Eichberger and Kelsey (J Econ Theory 106:436–466, 2002). In addition, we note that subjects’ ambiguity attitudes appear to be context dependent: ambiguity loving in single-person decisions and ambiguity averse in games. This is consistent with the findings of Kelsey and le Roux (Theory Decis 79:667–688, 2015).     

Learning-by-doing in an ambiguous environment

How well do revealed ambiguity preferences predict how people choose to seek new information about uncertain events? In an economics experiment, we apply a new instrument to measure ambiguity preferences, and in a later session observe to what extent the measure predicts the choice to receive costly information in a learning-by-doing game. Ambiguity averse subjects are more willing to pay to receive information, while risk averse subjects are not. Holding ambiguity preferences constant, risk averse subjects tend to perform worse than risk loving subjects. The returns to experimentation, especially for ambiguity averse subjects, suggest a not-well studied but important role that ambiguity preferences play in decision-making under uncertainty.     

Ellsberg paradox: Ambiguity and complexity aversions compared

We present a simple model where preferences with complexity aversion, rather than ambiguity aversion, resolve the Ellsberg paradox. We test our theory using laboratory experiments where subjects choose among lotteries that “range” from a simple risky lottery, through risky but more complex lotteries, to one similar to Ellsberg’s ambiguity urn. Our model ranks lotteries according to their complexity and makes different—at times contrasting—predictions than most models of ambiguity in response to manipulations of prizes. The results support that complexity aversion preferences play an important and separate role from beliefs with ambiguity aversion in explaining behavior under uncertainty.     

A taxonomy of all ordinal 2 × 2 games

The 2 × 2 game is the simplest and most commonly employed representation of strategic conflict. The 78 strict ordinal 2 × 2 games have been used as conflict models extensively, and have been related in several different taxonomies. However, interest has recently focussed on the full set of 726 general ordinal games, in which one or both players may have equal preferences for two or more outcomes. This paper describes the development of a practical taxonomy of all 726 ordinal 2 × 2 games. The taxonomy provides for rapid identification of particular games, gives a convenient ordering, is as consistent as possible with previous work, and yet is not tied to any specific solution concepts. As well, definitions of several significant game properties are developed or extended to general ordinal games and applied in conjunction with the taxonomy.     

Tacit Coordination in Choice Between Certain Outcomes in Endogenously Determined Lotteries

Tacit coordination is studied in a class of games in which each of n = 20 players is required to choose between two courses of actions. The first action offers each player a fixed outcome whereas the second presents her the opportunity of participating in a lottery with probabilities that are determined endogenously. Across multiple iterations of the game and trial-to-trial changes in the composition of the lottery, we observe a remarkably good coordination on the aggregate but not individual level. We further observe systematic deviations from the Nash equilibrium solution that are accounted for quite well by a simple adaptive learning model.     

Ambiguity aversion and familiarity bias: Evidence from behavioral and gene association studies

It is increasingly recognized that decision making under uncertainty depends not only on probabilities, but also on psychological factors such as ambiguity and familiarity. Using 325 Beijing subjects, we conduct a neurogenetic study of ambiguity aversion and familiarity bias in an incentivized laboratory setting. For ambiguity aversion, 49.4% of the subjects choose to bet on the 50–50 deck despite the unknown deck paying 20% more. For familiarity bias, 39.6% choose the bet on Beijing’s temperature rather than the corresponding bet with Tokyo even though the latter pays 20% more. We genotype subjects for anxiety-related candidate genes and find a serotonin transporter polymorphism being associated with familiarity bias, but not ambiguity aversion, while the dopamine D5 receptor gene and estrogen receptor beta gene are associated with ambiguity aversion only among female subjects. Our findings contribute to understanding of decision making under uncertainty beyond revealed preference.     

LEXICOGRAPHIC ADDITIVITY FOR MULTI-ATTRIBUTE PREFERENCES ON FINITE SETS

Payoff dominance, a criterion for choosing between equilibrium points in games, is intuitively compelling, especially in matching games and other games of common interests, but it has not been justified from standard game-theoretic rationality assumptions. A psychological explanation of it is offered in terms of a form of reasoning that we call the Stackelberg heuristic in which players assume that their strategic thinking will be anticipated by their co-player(s). Two-person games are called Stackelberg-soluble if the players' strategies that maximize against their co-players' best replies intersect in a Nash equilibrium. Proofs are given that every game of common interests is Stackelberg-soluble, that a Stackelberg solution is always a payoff-dominant outcome, and that in every game with multiple Nash equilibria a Stackelberg solution is a payoff-dominant equilibrium point. It is argued that the Stackelberg heuristic may be justified by evidentialist reasoning.     

Bargaining strength in three-person characteristic-function games with v(i)> 0 a reanalysis of Kahan and Rapoport (1977)

Kahan and Rapoport (1977) investigated the effects of guaranteed payoffs on bargaining in three-person cooperative games by systematically varying different sources of power: the power arising from the 1-person values, the power emerging from the pair coalitions as reflected by the quotas of the non-normalized game, and the grand coalition value. In the present paper it is suggested that one additionally take into account the assumption of strategic equivalence and that one analyze games with v(i)>0 in terms of the quotas of the zero-normalized game. Ostmann's (1984) rather sophisticated game theoretic framework, permitting the standardization of all three-person games, is introduced. A reanalysis of Kahan and Rapoport's data employing this perspective yields results which can be interpreted more easily than those of the original study. Moreover, they are consistent with the findings of almost all studies on 3-person characteristic-function games. It is argued that one could use the introduced analytical framework to investigate the range of empirical validity of the mathematical assumption of invariance under strategic equivalence.     

Spatial externalities and risk in interdependent security games

Individuals regularly invest in self-protection to reduce the risk of an adverse event. The effectiveness of self-protection often depends on the actions of other economic agents and can be modeled as a stochastic coordination game with multiple Pareto-ranked equilibria. We use lab experiments to analyze tacit coordination in stochastic games with two kinds of interdependencies in payoffs: “non-spatial” in which every agent’s action has an impact on the risk faced by every other agent, and “spatial” in which agents only impact the risk faced by their immediate neighbors. We also compare behavior in the stochastic games to deterministic versions of the same games. We find that coordination on the payoff-dominant equilibrium is significantly easier in the deterministic games than in the stochastic games and that spatial interdependencies lead to greater levels of coordination in the deterministic game but not in the stochastic game. The difficulty with coordination observed in the stochastic games has important implications for many real-world examples of interdependent security and also illustrates the importance of not relying on data from deterministic experiments to analyze behavior in settings with risk.     

Stochastic Evolution of Rules for Playing Finite Normal Form Games

The evolution of boundedly rational rules for playing normal form games is studied within stationary environments of stochastically changing games. Rules are viewed as algorithms prescribing strategies for the different normal form games that arise. It is shown that many of the “folk results” of evolutionary game theory, typically obtained with a fixed game and fixed strategies, carry over to the present environments. The results are also related to some recent experiments on rules and games.      

Outsourcing with identical suppliers and shortest-first policy: a laboratory experiment

We study experimentally in the laboratory two 2-player games that mimic a decentralized decision-making situation in which firms repeatedly outsource production orders to multiple identical suppliers. The first game has a unique (inefficient) equilibrium in mixed strategies, while the second game has two (efficient) equilibria in pure strategies and an infinite number of (inefficient) equilibria in mixed strategies. In both games, the optimal social costs can also be obtained via dominated strategies. We find that only in the second game subjects manage to reach an efficient outcome more often when matched in fixed pairs than when randomly rematched each round. Surprisingly, this is because subjects coordinate on dominated strategies (and not an efficient pure strategy equilibrium). We show theoretically that preferences for efficiency cannot explain our experimental results. Inequality aversion, on the other hand, cannot be rejected.     

A choice for ‘me’ or for ‘us’? Using we-reasoning to predict cooperation and coordination in games

Cooperation is the foundation of human social life, but it sometimes requires individuals to choose against their individual self-interest. How then is cooperation sustained? How do we decide when instead to follow our own goals? I develop a model that builds on Bacharach (in: Gold, Sugden (eds) Beyond individual choice: teams and frames in game theory, 2006) ??circumspect we-reasoning?? to address these questions. The model produces a threshold cost/benefit ratio to describe when we-reasoning players should choose cooperatively. After assumptions regarding player types and beliefs, we predict how the extent of cooperation varies across games. Results from two experiments offer strong support to the models and predictions herein.     

精神家园的迷失：远离自然的儿童游戏--基于柳溪村儿童游戏的田野调查

在幼儿游戏方面,柳溪村幼儿班里年纪较小的孩子们在幼师和家长的视野之外,建构了独立自由的游戏空间,从而区隔了课上与课下的二元游戏界限———唯有在课下“真空”的游戏场域中,孩子们的游戏精神方能发挥到淋漓尽致。但从乡村儿童总体的游戏情形来看：传统的儿童游戏几近衰落,手工制作玩具濒临失传。这些伴随电子游戏成长起来的乡村儿童,面临着比城市儿童更严重的电视依赖,他们游戏的性质经历了从亲近自然到远离自然、从手工创意制作到购买廉价玩具、从群体嬉戏到个体自娱、从动态游戏到静态娱乐的异化过程。     

Judged knowledge and ambiguity aversion

Competence has recently been proposed as an explanation for the degree of ambiguity aversion. Using general knowledge questions we presented subjects with simple lotteries in which they could bet on an event and against the same event. We show that the sum of certainty equivalents for both bets depends on the judged knowledge of the class of events. We also elicited the decision weights for events and complementary events. We found a similar effect of knowledge on the sum of decision weights.     

Ellsberg games

In the standard formulation of game theory, agents use mixed strategies in the form of objective and probabilistically precise devices to conceal their actions. We introduce the larger set of probabilistically imprecise devices and study the consequences for the basic results on normal form games. While Nash equilibria remain equilibria in the extended game, there arise new Ellsberg equilibria with distinct outcomes, as we illustrate by negotiation games with three players. We characterize Ellsberg equilibria in two-person conflict and coordination games. These equilibria turn out to be related to experimental deviations from Nash equilibrium play.     

Equilibria for far-sighted players

A new equilibrium concept for non-cooperative games, based on the assumptions that players are rational and far-sighted, is examined. An outcome is extended non-myopically (XNM) stable for a player if that player is assured that no movecountermove sequence he could initiate by departing unilaterally from that outcome would benefit him. The extended non-myopic (XNM) equilibria of a game, the outcomes which are XNM stable for each player, therefore model permanent (enduring) equilibria in an ongoing conflict.Algorithms for the identification of XNM equilibria in a 2 × 2 game are presented. The XNM concepts are then applied to three special classes of games (no-conflict games, games of complete opposition, and strict ordinal games) to compare their predictions of long-term stability with the known properties of games in these classes.Research supported by Natural Sciences and Engineering Research Council of Canada Grant No. A8974.     

From Keynes to a theoretical-political approach to conventional economics

The aim of this study is twofold. The first is to question the claim that the price system is the only form of coordination of individual actions. The attempt to overcome this assumption highlights the need for other forms of coordination to regulate behaviours that are not price-related, proposing the concept of Keynesian Convention as a special kind of coordination. The second is an effort to define the theoretical-political dimension of the economics of conventions. In fact, focusing on the strategic approach of conventions, depending on whether the concept of a convention is used to resolve problems finding a balance in coordination games, it seems reasonable to seek a political dimension of the economics of conventions. We will show how the assumptions underlying the theory of general economic balance are extremely restrictive, because they assume a complete lack of uncertainty or strategic interaction between the different agents. For the purpose of ensuring objectivity, we will highlight the role of the concept of the convention as a mechanism of coordination that transcends prices. Finally, although the standard theory strives to prove otherwise, the narrow path of validation is proof that an analysis of coordination cannot consider only the price system and is inseparable from the concept of rules.