Payoff Information Research Articles

Payoff Information Biases a Fast Guess Process in Perceptual Decision Making under Deadline Pressure: Evidence from Behavior, Evoked Potentials, and Quantitative Model Comparison.

Humans and other animals often face situations in which they must make choices based on uncertain sensory information together with information about expected outcomes (gains or losses) about each choice. We investigated how differences in payoffs between available alternatives affect neural activity, overt choice, and the timing of choice responses. In our experiment, in which participants were under strong time pressure, neural and behavioral findings together with model fitting suggested that our human participants often made a fast guess toward the higher reward rather than integrating stimulus and payoff information. Our findings, taken with findings from other studies, support the idea that payoff and prior probability manipulations produce flexible adaptations to task structure and do not reflect a fixed policy.

An Adaptive Learning Model with Foregone Payoff Information

AbstractIn this paper, we provide theoretical predictions on the long-run behavior of an adaptive decision maker with foregone payoff information. In the model, the decision maker assigns a subjective payoff assessment to each action based on his past experience and chooses the action that has the highest assessment. After receiving a payoff, the decision maker updates his assessments of actions in an adaptive manner, using not only the objective payoff information but also the foregone payoff information, which may be distorted. The distortion may arise from “the grass is always greener on the other side” effect, pessimism/optimism or envy/gloating; it depends on how the decision maker views the source of the information. We first provide conditions in which the assessment of each action converges, in that the limit assessment is expressed as an average of the expected objective payoff and the expected distorted payoff of the action. Then, we show that the decision maker chooses the optimal action most frequently in the long run if the expected distorted payoff of the action is greater than the ones of the other actions. We also provide conditions, under which this model coincides with the experience-weighted attraction learning, stochastic fictitious play and quantal response equilibrium models, and thus this model provides theoretical predictions for the models in decision problems.

Information Sharing to Reduce Misperceptions of Interactions Among Complementary Projects: A Multi-Agent Approach

Agents who invest periodically in two complementary projects i and j try to minimize shortfall due to misperceptions concerning the interaction α between i and j. Previous studies have analytically solved such problems but they have been limited to two agents making one decision. We set out with the hypothesis of a large number of deciders sharing information with their nearest neighbors in order to improve the understanding of α. After each period of time, they exchange information on their real payoff values which enables them to choose the best neighbor expected perception of α in order to minimize their shortfall. To model this situation, we used an agent-based approach and we considered that the payoff information transmission was more or less efficient depending on the difficulty to assess the real values or when agents voluntarily transfer wrong data to their neighbors. Our simulation results showed that the total shortfall of the network: i.) declines when α is overestimated, ii.) depends on the initial agent's opinions about α, iii.) evolves in two different curve morphologies, iv.) is influenced by the quality of information and can express a high heterogeneity of final opinions and v.) declines if the size of the neighborhood increases, which is a counterintuitive result.

Cooperation in spatial prisoner’s dilemma game with delayed decisions

Phenomena that time delays of information lead to delayed decisions are extensive in reality. The effect of delayed decisions on the evolution of cooperation in the spatial prisoner’s dilemma game is explored in this work. Players with memory are located on a two dimensional square lattice, and they can keep the payoff information of his neighbors and his own in every historic generation in memory. Every player uses the payoff information in some generation from his memory and the strategy information in current generation to determine which strategy to choose in next generation. The time interval between two generations is set by the parameter m. For the payoff information is used to determine the role model for the focal player when changing strategies, the focal player’s decision to learn from which neighbor is delayed by m generations. Simulations show that cooperation can be enhanced with the increase of m. In addition, just like the original evolutionary game model (m=0), pretty dynamic fractal patterns featuring symmetry can be obtained when m>0 if we simulate the invasion of a single defector in world of cooperators on square lattice.

On informational nudging and control of payoff-based learning

We investigate a model of informational nudging in a context inspired by repeated games in traffic. Starting from a simple payoff–based learning model for an individual decision–maker (DM) choosing among multiple alternatives, we introduce a recommender who provides possibly misleading payoff information for unchosen options, so as to drive the DM's preferences to a desired equilibrium. This kind of white lie on the part of the recommender can be seen as an informational nudge in the sense of Thaler & Sunstein, and may thus arguably present some benefits over monetary incentive–based strategies for the purposes of planning. Considering the fluid limit of our simplified model, we show that the recommender can create (but not necessarily globally stabilize) any outcome he desires using constant lying strategies. We also identify a framing effect, in the sense that lies about the least favorable option has a different effect compared to lies on most favorable option.

Is Payoff Necessarily Weighted by Probability When Making a Risky Choice? Evidence from Functional Connectivity Analysis

How people make decisions under risk remains an as-yet-unresolved but fundamental question. Mainstream theories about risky decision making assume that the core processes involved in reaching a risky decision include weighting each payoff or reward magnitude by its probability and then summing the outcomes. However, recently developed theories question whether payoffs are necessarily weighted by probability when making a risky choice. Using functional connectivity analysis, we aimed to provide neural evidence to answer whether this key assumption of computing expectations holds when making a risky choice. We contrasted a trade-off instruction choice that required participants to integrate probability and payoff information with a preferential choice that did not. Based on the functional connectivity patterns between regions in which activity was detected during both of the decision-making tasks, we classified the regions into two networks. One network includes primarily the left and right lateral prefrontal cortices and posterior parietal cortices, which were found to be related to probability in previous reports, and the other network is composed of the bilateral basal ganglia, which have been implicated in payoff. We also found that connectivity between the payoff network and some regions in the probability network (including the left lateral prefrontal cortices and bilateral inferior parietal lobes) were stronger during the trade-off instruction choice task than during the preferential choice task. This indicates that the functional integration between the probability and payoff networks during preferential choice was not as strong as the integration during trade-off instruction choice. Our results provide neural evidence that the weighting process uniformly predicted by the mainstream theory is unnecessary during preferential choice. Thus, our functional integration findings can provide a new direction for the investigation of the principles of risky decision making.

Leader‐driven distortion of probability and payoff information affects choices between risky prospects

AbstractResearch indicating that decision makers often distort new information to favor nascent preferences has focused primarily on riskless choice rather than risky choice. In addition, the critical assumption that information distortion mediates the link between the initially preferred alternative and the final choice has not been tested in a compelling manner. In an experiment designed to fill these gaps, participants made six choices involving pairs of hypothetical three‐outcome monetary gambles. We manipulated initial preferences by varying the order in which gamble features were presented. Multilevel regressions indicated that participants distorted their evaluations of precise probabilities and payoffs in the direction of their emerging preferences and that they used their biased evaluations to update those preferences. As expected, information distortion mediated the effect of initial preferences on final choices and final preference strength. In a follow‐up experiment, we compared a standard measure of information distortion (based on comparisons to mean ratings in a no‐choice control task) to a more personalized measure (based on participants' own ratings in the control task) and found the mean‐based measure to be superior for the probability and payoff information in question. Other findings in Experiment 2 corroborated the results of Experiment 1. In both studies, the distortion of quantitative inputs in a simple task highlights the non‐normative circularity of the choice process. Copyright © 2010 John Wiley & Sons, Ltd.

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.

The Source and Significance of Confusion in Public Goods Experiments

Abstract Economists use public goods experiments to develop and test theories of individual preferences and institutional design. Previous work demonstrates many participants in public goods experiments contribute to the public good out of confusion. We design experiments to provide insights on the consequences and causes of confusion. We establish that confusion amounts to more than statistical noise and does not dissipate with repetition (i.e. learning). Confused subjects use experimental parameters and the behavior of other players as cues, which confounds treatment effects and traditional strategies to identify other-regarding preferences through exogenous parameter changes and the modeling of reactions to other subjects’ decisions. We argue that confusion stems from an inaccurate understanding of game incentives (“failure of game form recognition”), which is a consequence of the framing and inadequate payoff information in standard instructions. Modified instructions can substantially reduce confusion, and, in turn, change the distribution of contributions to the public good.

Coalitional game with fuzzy payoffs and credibilistic core

As an important branch of game theory, coalitional game deals with situations that involve cooperation among the players. This paper deals with this topic further by incorporating the fuzzy payoff information. Based on the credibility theory, we introduce two decision criteria to define the preferences of players, which leads to two definitions of credibilistic cores--the solution of coalitional game with fuzzy transferable payoffs. Meanwhile, we give a sufficient and necessary condition to ensure non-emptiness of the credibilistic cores. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.

Ambient-Based Policy Instruments: The Role of Recommendations and Presentation

We explore the effects of recommended play and the presentation of payoff information on behavior in an ambient-based policy instrument experiment. Specifically, we test the effects of recommended play (via a description of marginal decision making) and a payoff table on the behavior of individuals facing an ambient-based policy instrument. We find that recommended play and the presentation of a payoff table increases the use of the socially optimal strategy, thereby increasing efficiency. These results suggest that providing decision makers with a richer description of the decision making environment significantly reduces decision error, significantly improving the efficiency of ambient-based policy instruments.

Integration of Sensory and Reward Information during Perceptual Decision-Making in Lateral Intraparietal Cortex (LIP) of the Macaque Monkey

Single neurons in cortical area LIP are known to carry information relevant to both sensory and value-based decisions that are reported by eye movements. It is not known, however, how sensory and value information are combined in LIP when individual decisions must be based on a combination of these variables. To investigate this issue, we conducted behavioral and electrophysiological experiments in rhesus monkeys during performance of a two-alternative, forced-choice discrimination of motion direction (sensory component). Monkeys reported each decision by making an eye movement to one of two visual targets associated with the two possible directions of motion. We introduced choice biases to the monkeys' decision process (value component) by randomly interleaving balanced reward conditions (equal reward value for the two choices) with unbalanced conditions (one alternative worth twice as much as the other). The monkeys' behavior, as well as that of most LIP neurons, reflected the influence of all relevant variables: the strength of the sensory information, the value of the target in the neuron's response field, and the value of the target outside the response field. Overall, detailed analysis and computer simulation reveal that our data are consistent with a two-stage drift diffusion model proposed by Diederich and Bussmeyer [1] for the effect of payoffs in the context of sensory discrimination tasks. Initial processing of payoff information strongly influences the starting point for the accumulation of sensory evidence, while exerting little if any effect on the rate of accumulation of sensory evidence.

Simulating Social Network Formation

Social networks depict complex systems as graph theoretic models. The study of the formation of such systems (or networks) and the subsequent analysis of the network structures are of great interest. For information systems research and its impact on business practice, the ability to model and simulate a system of individuals interacting to achieve a certain socio-economic goal holds much promise for proper design and use of cyber networks. We use case-based decision theory to formulate a customizable model of information gathering in a social network. In this model, the agents in the network have limited awareness of the social network in which they operate and of the fixed, underlying payoff structure. Agents collect payoff information from neighbors within the prevailing social network, and they base their networking decisions on this information. Along with the introduction of the decision theoretic model, we developed software to simulate the formation of such networks in a customizable context to examine how the network structure can be influenced by the parameters that define social relationships. We present computational experiments that illustrate the growth and stability of the simulated social networks ensuing from the proposed model. The model and simulation illustrates how network structure influences agent behavior in a social network and how network structures, agent behavior, and agent decisions influence each other.

The Efficiency of Direct Public Involvement in Environmental Policymaking: An Experimental Test

In collaborative negotiation, stakeholder representatives are charged with the development of a mutually acceptable set of public policies. Although this approach has become popular in environmental negotiations, little is known about the characteristics of the outcomes that are reached. In this paper, we employ an Edgeworth box framework to investigate the nature of bargaining over public goods (environmental policies) that have multiple attributes. We then design and conduct laboratory experiments within this framework to test whether negotiated outcomes satisfy standard axiomatic bargaining predictions under a variety of conditions. Specifically, we test whether two parties with Pareto inefficient endowments of two goods will trade to Pareto improving and Pareto efficient outcomes, and to the Nash bargain in particular. We vary whether the Nash bargain coincides with or diverges from the outcome that maximizes the joint payoff, or the outcome that equalizes payoffs, and whether subjects are provided full or partial information. We find that bargainers reach Pareto improving and efficient outcomes across treatments, but withdraw support for the Nash bargain when it generates unequal payments or when payoff information is private. We conclude that this experimental framework offers a promising method for studying multi-attribute negotiations.

Does Money Illusion Matter? An Experimental Approach

Money illusion means that people behave differently when the same objective situation is represented in nominal or in real terms. To examine the behavioral impact of money illusion we studied the adjustment process of nominal prices after a fully anticipated negative nominal shock in an experimental setting with strategic complementarity. We show that seemingly innocuous differences in payoff presentation cause large behavioral differences. In particular, if the payoff information is presented to subjects in nominal terms, price stickiness and real effects are much more pronounced than when payoff information is presented in real terms. The driving force of differences in real outcomes is subjects’ expectation of higher nominal inertia in the nominal payoff condition. Due to strategic complementarity, these expectations induce subjects to adjust rather slowly to the shock.

Individual Differences in EWA Learning With Partial Payoff Information

We extend experience-weighted attraction (EWA) learning to games in which only the set of possible foregone payoffs from unchosen strategies are known, and estimate parameters separately for each player to study heterogeneity. We assume players estimate unknown foregone payoffs from a strategy, by substituting the last payoff actually received from that strategy, by clairvoyantly guessing the actual foregone payoff, or by averaging the set of possible foregone payoffs conditional on the actual outcomes. All three assumptions improve predictive accuracy of EWA. Individual parameter estimates suggest that players cluster into two separate subgroups (which differ from traditional reinforcement and belief learning).

Learning payoff functions in infinite games

We consider a class of games with real-valued strategies and payoff information available only in the form of data from a given sample of strategy profiles. Solving such games with respect to the underlying strategy space requires generalizing from the data to a complete payoff-function representation. We address payoff-function learning as a standard regression problem, with provision for capturing known structure (e.g., symmetry) in the multiagent environment. To measure learning performance, we consider the relative utility of prescribed strategies, rather than the accuracy of payoff functions per se. We demonstrate our approach and evaluate its effectiveness on two examples: a two-player version of the first-price sealed-bid auction (with known analytical form), and a five-player market-based scheduling game (with no known solution). Additionally, we explore the efficacy of using relative utility of strategies as a target of supervised learning and as a learning model selector. Our experiments demonstrate its effectiveness in the former case, though not in the latter.

Foregone with the Wind: Indirect Payoff Information and its Implications for Choice

Examination of the effect of information concerning foregone pay- offs on choice behavior reveals a complex pattern. Depending on the environ- ment, this information can facilitate or impair maximization. Our study of nine experimental tasks suggests that the complex pattern can be summarized with the assumption that initially people tend to be highly sensitive, and sometimes too sensitive, to recent foregone payoffs. However, over time, people can learn to adjust their sensitivity depending on the environment they are facing. The implicationsofthisobservationtomodelsofhumanadaptationandtoproblems of mechanism design are discussed.

Information selectivity in decision making by younger and older adults

Past research has demonstrated that older adults are more likely than younger adults to exhibit information selectivity in decision making. Two alternative explanations have been proposed to account for this age difference. One explanation attributes the increase in information selectivity to older adults' reliance on prior knowledge, whereas the other explanation suggests that it reflects reduced information processing capacity. The aim of this research was to explore the latter explanation by controlling for experiential factors and varying the cognitive demands involved in decision making. Specifically, participants were faced with unfamiliar decision problems, and had to base their decisions on the available information in order to reach a desired goal. In Experiment 1 younger and older participants were required to play a game involving chance. The outcome payoff was varied between three conditions (approach, avoidance, and control). The results indicated that both the younger and the older participants based their decisions on payoff, though the older participants did so to a lesser extent. In Experiment 2 younger and older participants performed a similar decision task but with higher cognitive demands. Specifically, the decision‐making task included two dimensions of information, outcome probability and outcome payoff. The results showed that the younger participants based their decisions on probability and payoff whereas the older participants based their decisions on probability alone. In Experiment 3 younger and older participants made decisions in a sale context and received instructional cue to incorporate payoff information in their decisions. As before, the younger participants utilized probability and payoff, whereas the older participants based their decisions only on probability information. The findings are discussed in terms of age differences in information‐processing capacity, metacognition, motivation, and goal‐setting.

Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games

Most learning models assume players are adaptive (i.e., they respond only to their own previous experience and ignore others' payoff information) and behavior is not sensitive to the way in which players are matched. Empirical evidence suggests otherwise. In this paper, we extend our adaptive experience-weighted attraction (EWA) learning model to capture sophisticated learning and strategic teaching in repeated games. The generalized model assumes there is a mixture of adaptive learners and sophisticated players. An adaptive learner adjusts his behavior the EWA way. A sophisticated player rationally best-responds to her forecasts of all other behaviors. A sophisticated player can be either myopic or farsighted. A farsighted player develops multiple-period rather than single-period forecasts of others' behaviors and chooses to “teach” the other players by choosing a strategy scenario that gives her the highest discounted net present value. We estimate the model using data from p-beauty contests and repeated trust games with incomplete information. The generalized model is better than the adaptive EWA model in describing and predicting behavior. Including teaching also allows an empirical learning-based approach to reputation formation which predicts better than a quantal-response extension of the standard type-based approach. Journal of Economic Literature Classification Numbers: C72, C91.