Melioration behaviour in the Harvard game is reduced by simplifying decision outcomes

Self-control experiments have previously been highlighted as examples of suboptimal decision making. In one such experiment, the Harvard game, participants make repeated choices between two alternatives. One alternative has a higher immediate pay-off than the other, but with repeated choices results in a lower overall pay-off. Preference for the alternative with the higher immediate pay-off seems to be impulsive and will result in a failure to maximize pay-offs. We report an experiment that modifies the Harvard game, dividing the pay-off from each choice into two separate consequences—the immediate and the historic components. Choosing the alternative with the higher immediate pay-off ends the session prematurely, leading to a loss of opportunities to earn further pay-offs and ultimately to a reduced overall pay-off. This makes it easier for participants to learn the outcomes of their actions. It also provides the opportunity for a further test of normative decision making by means of one of its most specific and paradoxical predictions—that the truly rational agent should switch from self-control to impulsivity toward the end of the experimental sessions. The finding that participants maximize their expected utility by both overcoming impulsivity and learning to switch implies that melioration behaviour is not due to the lure of impulsivity, but due to the difficulty of learning which components are included in the pay-off schedules.     

Cooperation in repeated interactions: A systematic review of Centipede game experiments, 1992–2016

Cooperation is a fundamental form of social interaction, and turn-taking reciprocity one of its most familiar manifestations. The Centipede game provides a formal model of such alternating reciprocal cooperation, but a backward induction (BI) argument appears to prove logically that instrumentally rational players would never cooperate in this way. A systematic review of experimental research reveals that human decision makers cooperate frequently in this game, except under certain extreme conditions. Several game, situational, and individual difference variables have been investigated for their influence on cooperation. The most influential are aspects of the payoff function (especially the social gain from cooperation and the risk associated with a cooperative move), the number of players, repetitions of the game, group vs. individual decisions, and players’ social value orientations (SVOs). Our review of experimental evidence suggests that other-regarding preferences, including prosocial behavioural dispositions and collective rationality, provide the most powerful explanation for cooperation.     

Logic Games are Complete for Game Logics

Game logics describe general games through powers of players for forcing outcomes. In particular, they encode an algebra of sequential game operations such as choice, dual and composition. Logic games are special games for specific purposes such as proof or semantical evaluation for first-order or modal languages. We show that the general algebra of game operations coincides with that over just logical evaluation games, whence the latter are quite general after all. The main tool in proving this is a representation of arbitrary games as modal or first-order evaluation games. We probe how far our analysis extends to product operations on games. We also discuss some more general consequences of this new perspective for standard logic.     

What you don’t know won’t hurt me: Costly (but quiet) exit in dictator games

We used simple economic games to examine pro-social behavior and the lengths that people will take to avoid engaging in it. Over two studies, we found that about one-third of participants were willing to “exit” a $10 dictator game and take $9 instead. The exit option left the receiver nothing, but also ensured that the receiver never knew that a dictator game was to be played. Because most social utility models are defined over monetary outcomes, they cannot explain choosing the ($9, $0) exit outcome over the dominating $10 dictator game, since the game includes outcomes of ($10, $0) and ($9, $1). We also studied exiting using a “private” dictator game. In the private game, the receiver never knew about the game or from where any money was received. Gifts in this game were added innocuously to a payment for a separate task. Almost no dictators exited from the private game, indicating that receivers’ beliefs are the key factor in the decision to exit. When, as in the private game, the receivers’ beliefs and expectations cannot be manipulated by exit, exit is seldom taken. We conclude that giving often reflects a desire not to violate others’ expectations rather than a concern for others’ welfare per se. We discuss the implications of our results for understanding ethical decisions and for testing and modeling social preferences. An adequate specification of social preferences should include “psychological” payoffs that directly incorporate beliefs about actions into the utility function.     

Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game

Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two‐player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes.     

The politics of careers education and guidance: A case for scrutiny

Political aspects of processes involved in defining careers education and guidance are brought to light through an examination of debates surrounding the definition of guidance at four different points of the journey from policy to practice, and of related 'gaps' between 'theory' and 'practice'. It is argued that these 'gaps' cannot be adequately conceptualised within a curriculum evaluation paradigm. They result from the conflictual nature of curriculum change which, in this case, produced repeated contests over the definition of guidance, with different outcomes in different occupational settings. These outcomes, it is argued, were influenced not only by rational debate but by the distribution of power between the various groups of actors concerned. The politics of careers education and guidance are placed on the agenda for consideration by both researchers and practitioners.     

On fairness and learning agents in a bargaining model with uncertainty

The emergence of fair divisions in a repeated bargaining game is investigated in a computational model. Individuals of human societies often appeal to some norm of fairness in situations where an agreement over the division of a surplus is required. The employed framework consists of players alternating offers that describe possible ways to share a certain commodity. The players are allowed a limited number of offers to reach an agreement; if they fail to agree, the player who made the first offer, the lucky player, wins the whole lot at stake. Uncertainty is introduced in the process by randomly choosing the lucky player at the beginning of each iteration. In the experiments, the players acquired strategies by employing a variant of Q-learning, a reinforcement learning algorithm. Experiments were performed with different configurations of utility functions on the players’ preferences in taking actions in risky situations. Analysis of the results shows that the game theoretical model of a single shot of the bargaining game used in the experiments closely matches the outcomes obtained in the simulated framework, despite the differences in the quality of the players, who are assumed to be fully rational in the theoretical model. Learning agents that are timid toward risky situations manage to acquire strategies that lead to fair outcomes when playing against each other, but find themselves in a disadvantageous position when confronting bolder types.     

PC-Based Game Features That Influence Instruction and Learner Motivation

PC-based games are currently being used for military training, but the instructional and motivational features of such technology are not well understood. To identify features of training games that influence instruction and motivation, a popular first-person-perspective game with a military theme was analyzed empirically. Twenty-one participants played the “basic training” portion of the game, which included Army background information, virtual marksmanship training, an obstacle course, virtual weapons familiarization, and an urban terrain training mission. The results of this research provide useful information to individuals developing training games, desktop simulations, and interactive multimedia courseware to meet optimal training objectives and strategies.     

Ontology in the Game of Life

The game of life is an excellent framework for metaphysical modeling. It can be used to study ontological categories like space, time, causality, persistence, substance, emergence, and supervenience. It is often said that there are many levels of existence in the game of life. Objects like the glider are said to exist on higher levels. Our goal here is to work out a precise formalization of the thesis that there are various levels of existence in the game of life. To formalize this thesis, we develop a set-theoretic construction of the glider. The method of this construction generalizes to other patterns in the game of life. And it can be extended to more realistic physical systems. The result is a highly general method for the set-theoretical construction of substances.     

Subgames within Large Games and the Heuristic of Imitation

We study repeated normal form games where the number of players is large. We argue that it is interesting to look at such games as being divided into subgames, each of which we call a neighbourhood. The structure of such a game is given by a graph G whose nodes are players and edges denote visibility. The neighbourhoods are maximal cliques in G. The game proceeds in rounds where in each round the players of every clique X of G play a strategic form game among each other. A player at a node v strategises based on what she can observe, i.e., the strategies and the outcomes in the previous round of the players at vertices adjacent to v. Based on this, the player may switch strategies in the same neighbourhood, or migrate to another neighbourhood. We are interested in addressing questions regarding the eventual stability of such games. We incrementally impose constraints on the ‘types’ of the players. First, we look at players who are unconstrained in their strategising abilities, in that, players who may use unbounded memory. We then consider the case of memoryless players. We show that in both these cases the eventual stability of the game can be characterised in terms of potentials. We then introduce a simple modal logic in which the types of the players can be specified. We show that when the players play according to these specified types, it can be effectively decided whether the game stabilises. Finally, we look at the important heuristic of imitation. Simple imitative strategies can be specified in the logic introduced by us. We show that in a population of optimisers and imitators, we can decide how ‘worse-off’ the imitators are by playing imitative strategies rather than optimal ones.     

信任还是设防？互动博弈中社会善念对合作行为的促进效应

社会善念是个体在人际互动中充满善意地关注、尊重并保护他人选择的需要和权利的行为,通过实施社会善念有助于提升他人的合作行为。为检验这一假设,本实验设置了“施—受”双方的互动博弈情境,采用“物品选择游戏”操纵实施者的社会善念水平,分别利用信任博弈和公共物品游戏测查接受者在互动过程中的信任水平和合作行为。结果发现：相比于低社会善念组,被试在高社会善念组中表现出更高的信任水平和合作行为。进一步路径分析也发现,信任在感知社会善念与合作行为间发挥着部分中介作用。由此可见,社会善念行为的实施为互动双方建立信任关系提供了重要线索,降低了人们时时“设防”的监控动机,使合作带来的利益双赢成为可能。     

When things don't add up: the role of perceived fungibility in repeated-play decisions

Previous research on repeated-play decisions has focused on choices with fungible outcomes. We investigated the perceived fungibility of outcomes over repeated plays of risky prospects in several situations, as well as the relationship between perceived fungibility and preferences for taking risks in those situations. Perceived fungibility varied substantially across participants and situations, with outcomes experienced by different people (e.g., medical outcomes for different patients) receiving lower scores than outcomes experienced by a single person. Higher perceived fungibility was associated with more favorable evaluations of repeated plays of risky prospects with positive expectations. Additionally, perceived fungibility moderated the effect of repetition, such that the increased attractiveness of repeated plays relative to a single play was diminished when perceived fungibility was low. Although evaluating the overall distribution of outcomes is arguably rational when monetary outcomes accrue to one person, treating each play as a separate event may be more appropriate when outcomes are not viewed as fungible.     

集体问题解决中的认知表征、行为惯例和动态能力

以王建安和张钢(2008)开发的三人TTT纸牌游戏(原游戏)及其变式(变式游戏)为实验任务, 研究了集体问解决中认知表征和行为惯例对提高动态能力的作用。共有240名被试, 分成80个三人小组, 参加了前后两场各20盘游戏。80个小组按照是否被告知游戏的问题表征(即有无认知表征), 以及是玩原游戏还是玩变式游戏, 均分成4个区组来玩第一场游戏。在第二场游戏中, 4个区组都玩变式游戏。以玩每盘游戏的平均步时和在问题表征中走过的路径为指标测量惯例, 以玩第一场原游戏习得的能力向玩第二场变式游戏的迁移率来衡量动态能力。结果发现：一方面, 适当的认知表征有助于提高集体问题解决的动态能力; 另一方面, 没有适当认知表征支持的行为惯例反而会阻碍动态能力的发展。概括地说, 动态能力的决定因素是认知表征而不是行为惯例。     

To be at the tail of the lions or the head of the foxes?

Agents seeking an opportunity for profit often have to compete with others who pursue the same opportunity. When having to choose between a number of opportunities differing in their value and if individuals differ in their chances of outperforming others, the choice can be cognitively and emotionally demanding. We explore choice between opportunities using stylized Lions–Foxes games. In such a game, each of three players, with different odds of beating others, has to choose one of two contests that offer different rewards. After game theoretically analyzing the games, which we have experimentally employed, we report four experiments that vary in choice elicitation (repeated play or strategy method), in players' matching (random strangers or partners) and in rewards. Regarding contest choices, we found the choice of the higher value (and seemingly more prestigious) contest to be positively related to winning odds, contrary to what four out of the five (mixed, partially mixed, or pure) equilibria predict. Participants started out rather optimistic, with a large majority choosing the higher value option, but with experience, they approached the only viable of two pure strategy equilibria. Still, mixing continued via reacting to past play and outcome, apparently balancing dissatisfaction from choosing either contest.     

Revisions and Regret: The Cost of Changing your Mind

Decision reversals often imply improved decisions. Yet, people show a strong resistance against changing their minds. These are well‐established findings, which suggest that changed decisions carry a subjective cost, perhaps by being more strongly regretted. Three studies were conducted to explore participants' regret when making reversible decisions and to test the hypothesis that changing one's mind will increase post‐outcome regret. The first two studies employed the Ultimatum game and the Trust game. The third study used a variant of the Monty Hall problem. All games were conducted by individual participants playing interactively against a computer. The outcomes were designed to capture a common characteristic of real‐life decisions: they varied from rather negative to fairly positive, and for every outcome, it was possible to imagine both more and less profitable outcomes. In all experiments, those who changed their minds reported much stronger post‐outcome regret than those who did not change, even if the final outcomes were equally good (Experiments 2 and 3) or better (Experiment 1).This finding was not because of individual differences with respect to gender, tendency to regret, or tendency to maximize. Previous studies have found that those who change from a correct to wrong option regret more than those who select a wrong option directly. This study indicates that this finding is a special case of a more general phenomenon: changing one's mind seems to come with a cost, even when one ends up with favorable outcomes. Copyright © 2011 John Wiley & Sons, Ltd.     

影响博弈结果的方法效应研究

最后通谍博弈和独裁者博弈是实验经济学的经典博弈,也被心理学家用来研究人的公平和利他行为。该研究考查了经济学和心理学通常的报酬支付方式、博弈中待分配的金额是否影响博弈结果,以及两个博弈进行组内实验时是否会产生顺序效应。结果发现支付方式和金额不影响博弈结果,但有顺序效应产生。该研究对国内研究者进一步借用这两个博弈的相关研究打下了一定的方法学基础。     

Effective choice in all the symmetric 2 × 2 games

Solution concepts for game play implicitly assume what information is relevant for choosing moves. Maximin and Eliminating Dominated Strategies use payoff order; mixed strategies and Harsanyi??s risk dominance use payoff values. ??Cooperative?? strategies use previous choices, ignoring payoffs altogether. We first define the 12 symmetric 2 × 2 games as a continuous payoff space then use this space to evaluate strategies based on different types of information. Strategic success is shown to be sensitive to actual payoffs and seldom consistent for all games of an ordinally defined category such as Chicken. A new hybrid strategy using both payoff and choice information is introduced and shown to produce efficient outcomes in all symmetric 2 × 2 games when employed by both players. It does well in evolutionary tournaments against strategies of other types, especially in the difficult distribution games including Battle-of-the-Sexes.     

When to (or not to) trust intelligent machines: Insights from an evolutionary game theory analysis of trust in repeated games

The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, users take the risk that such agents act in ways opposed to the users’ preferences or goals. It is often argued that people use trust as a cognitive shortcut to reduce the complexity of such interactions. Here we formalise this by using the methods of evolutionary game theory to study the viability of trust-based strategies in repeated games. These are reciprocal strategies that cooperate as long as the other player is observed to be cooperating. Unlike classic reciprocal strategies, once mutual cooperation has been observed for a threshold number of rounds they stop checking their co-player’s behaviour every round, and instead only check it with some probability. By doing so, they reduce the opportunity cost of verifying whether the action of their co-player was actually cooperative. We demonstrate that these trust-based strategies can outcompete strategies that are always conditional, such as Tit-for-Tat, when the opportunity cost is non-negligible. We argue that this cost is likely to be greater when the interaction is between people and intelligent agents, because of the reduced transparency of the agent. Consequently, we expect people to use trust-based strategies more frequently in interactions with intelligent agents. Our results provide new, important insights into the design of mechanisms for facilitating interactions between humans and intelligent agents, where trust is an essential factor.     

我会在谁面前舍弃利益?——博弈对象的能力与社会距离对名利博弈倾向的影响

通过构造虚拟的捐献情境及贸易情境,结合博弈任务,以大学生为被试探讨了名利博弈对象的能力和社会距离对名利博弈中博弈者的博弈行为倾向的影响。结果表明,在捐献情境下,被试在高能力的名利博弈对象面前比在低能力的名利博弈对象面前更倾向于做出接近自己半数报酬的捐献行为,牺牲利益以获取好名声。在贸易情境下存在名利博弈对象的能力与社会距离的交互作用,被试仅在面对低能力的名利博弈对象时会考虑社会距离因素,在社会距离近的名利博弈对象面前比在社会距离远的名利博弈对象面前提出更低的售价,牺牲自己的利益以获得好名声。研究结果初步证实名利博弈对象能力与社会距离对名利博弈具有重要影响以及个体在名利博弈中具有策略性。