Iterative Game Research Articles

Convergence to Equilibria in Plurality Voting

Multi-agent decision problems, in which independent agents have to agree on a joint plan of action or allocation of resources, are central to AI. In such situations, agents' individual preferences over available alternatives may vary, and they may try to reconcile these differences by voting. Based on the fact that agents may have incentives to vote strategically and misreport their real preferences, a number of recent papers have explored different possibilities for avoiding or eliminating such manipulations. In contrast to most prior work, this paper focuses on convergence of strategic behavior to a decision from which no voter will want to deviate. We consider scenarios where voters cannot coordinate their actions, but are allowed to change their vote after observing the current outcome. We focus on the Plurality voting rule, and study the conditions under which this iterative game is guaranteed to converge to a Nash equilibrium (i.e., to a decision that is stable against further unilateral manipulations). We show for the first time how convergence depends on the exact attributes of the game, such as the tie-breaking scheme, and on assumptions regarding agents' weights and strategies.

Sustaining iterative game playing processes in DGBL: The relationship between motivational processing and outcome processing

Digital game-based learning (DGBL) has become a viable instructional option in recent years due to its support of learning motivation. Recent studies have mostly focused on identifying motivational factors in digital games (e.g., curiosity, rules, control) that support intrinsic motivation. These findings, however, are limited in two fronts. First, they did not depict the interactive nature of the motivational processing in DGBL. Second, they excluded the outcome processing (learners’ final effort versus performance evaluation) as a possible motivation component to sustain the iterative game playing cycle. To address these problems, situated in the integrative theory of Motivation, Volition, and Performance (MVP), this study examined the relationship between motivational processing and outcome processing in an online instructional game. The study surveyed 264 undergraduate students after playing the Trade Ruler online game. Based on the data collected by ARCS-based Instructional Materials Motivational Survey (IMMS), a regression analysis revealed a significant model between motivational processing (attention, relevance, and confidence) and the outcome processing (satisfaction). The finding preliminarily suggests that both motivational processing and outcome processing need to be considered when designing DGBL. Furthermore, the finding implies a potential relationship between intrinsic motives and extrinsic rewards in DGBL.

Solving Cournot equilibriums with variational inequalities algorithms

Over the past two decades, the fact that many games have been formulated as variational inequalities problems has led to relevant developments related with the existence and uniqueness of equilibriums, and with their calculation methodologies. Based on this approach, this study applies sufficient conditions for Cournot equilibriums existence and uniqueness, proving that while existence holds, uniqueness cannot be proved in general. To find one of the existent equilibriums, this study also proposes a novel variational inequalities algorithm which is globally convergent and easy to implement. It iteratively computes searching directions of the equilibrium by generating hyper-planes that separate the equilibrium from the intermediate solutions obtained relaxing the original Cournot game. Unlike other related algorithms, the proposed algorithm does not require Jacobian matrixes evaluation, and the iterative relaxed games can easily be solved using convex and quadratic optimisation models. Numerical results show the operation and convergence of the algorithm.

Iterative game design in education

Educators should impart principles of iterative game design to their students as a best practice. Iterative processes allow player feedback to systematically inform design decisions. However, the constraints and conventions of academic practices pose several challenges for the adoption of iterative processes. Many students lack the confidence in their own abilities and the discipline to work in short iterations. A constant stream of testers is necessary for iterative design and providing that stream requires advance planning. Misinterpreting tester feedback can badly hurt morale. Finally, the tendency of both game development and academia to focus on a finished product may actually distract students from practicing the habits needed to conduct effective iterative design. Based on the student projects of the Singapore-MIT GAMBIT Game Lab, this short paper looks into each of these challenges and proposes some potential solutions for introducing iterative game design in a higher education context.

On Inferring Demand for Health Care in the Presence of Anchoring and Selection Biases

In the contingent valuation literature, anchoring bias poses problems when using an iterative bidding game to infer willingness to pay. This bias occurs when the willingness to pay estimate is sensitive to the initially presented starting value. More generally, whenever a survey format is used and not all of those contacted participate, selection bias raises concerns about the representativeness of the sample. In this paper, we estimate students' willingness to pay for student health care at Stanford University while accounting for both of these biases. As there is no cost sharing for students, we assess willingness to pay by having a random sample of students play an on line iterative bidding game. Our main results are that (1) demand for student health care is elastic by conventional standards; (2) ignoring anchoring bias would lead to a substantially biased measure of the demand elasticity; and (3) standard selection correction methods indicate no bias from selective non-response and newer bounding methods support this conclusion of elastic demand.

The α-beauty contest: Choosing numbers, thinking intervals

We present a model for the α-beauty contest that explains common patterns in experimental data of one-shot and iterative games. The approach is based on two basic assumptions. First, players iteratively update their recent guesses. Second, players estimate intervals rather than exact numbers to cope with incomplete knowledge of other players' rationality. Under these assumptions we extend the cognitive hierarchy model of Camerer et al. [Camerer, C., Ho, T., Chong, J., 2003b. A cognitive hierarchy model of one-shot games. Quart. J. Econ. 119, 861–898]. The extended model is estimated on experimental data from a newspaper experiment.

Reputational Risk and Enforceability in International Law

Reputational Risk and Enforceability in International Law Rachel A. Bahn The lack of an automatic enforcement mechanism represents the greatest challenge to the development of international organizations and the body of international public law that they represent. Evidence of the impact of this non-enforceability is found in all areas of the international realm—economic, humanitarian, and political-strategic. However, the nature of political-strategic affairs heightens the impact of possible damage to national reputation and sets this branch of international law and organization apart. The World Trade Organization (WTO) has no absolute means through which to ensure compliance with its standards, even when its Dispute Settlement Panel determines that a member state has violated the WTO’s international liability and must alter its behavior or face retaliation from the harmed state. More to the point, there is no absolute means to ensure compliance with WTO standards. One need only look to the gambling case brought against the United States by the Caribbean nation of Antigua and Barbuda in order to verify the ineffectiveness of WTO panel decisions. In 2003, Antigua and Barbuda brought a legitimate complaint to the WTO that the United States had improperly restricted the sale of online gaming and betting services from the island nation. Nevertheless, even after the complaint was raised, the United States, another WTO member state, refused to comply with WTO standards, due in part to domestic political and ethical concerns about gambling.1 Because Antigua and Barbuda has little leverage against the United States, its WTO-sanctioned countermeasures (to the tune of $221 million) have been ineffective, permitting the behemoth to continue barring the sale of gambling services across its national borders.2 Subsequent to the WTO ruling, the United States retroactively altered its commitment to the General Agreement on Trade in Services—effectively continuing to violate its previously agreed international economic obligations.3 Humanitarian bodies have proven no more adept at ensuring compliance with international norms and standards. The authority and eventual judgment of human rights tribunals may be flaunted by states unwilling to deliver the politically powerful to the judgment of the international community. For years, Serbia refused to deliver a number of suspected Serbian war criminals to the International Criminal Tribunal for the former Yugoslavia [End Page 101] so that their actions could be considered and judged on the international stage.4 (Included among these war criminals was Ratko Mladic, the Bosnian Serb general who was responsible for the massacre of nearly 8,000 Muslim men and boys at Srebrenica in 1995, and Radovan Karadzic, the former Serbian president.5 ) To date, Serbia has refused to directly deliver either Mladic or Karadzic. Both men remain fugitives from international law.6 The United Nations and the body of international humanitarian and political law that it represents are similarly at the mercy of member states that choose to enforce or disregard their agreed-upon commitments and obligations. This is most evident in the case of the Security Council, where a single member may utilize its veto block action on the part of the entire UN. Without an international police force to ensure compliance with the will of the majority, absolute compliance with international norms remains a hope rather than a certainty. If international relations are considered as an iterative game, the high stakes of security and military affairs paradoxically give the prospect of reputational risk greater persuasive power in ensuring compliance with international obligations. The United States has suffered dramatically in terms of international public opinion because of its war in Iraq, and in certain Muslim countries, because of its perceived acquiescence to Israel’s occupation of the West Bank and Gaza. More striking, the United States’ reputation is falling in stature in countries that have been traditional allies, as well as those who might prove invaluable as future allies, for example Turkey, Morocco, and Jordan.7 Unilateralism in international affairs—whether political, economic, humanitarian, or otherwise—is not merely a willingness to go it alone, but a wager that in the long term, the action in question will validate any short-term reputational damage. The wager of the United States in Iraq has yet to prove its worth, while in...

Game theoretic analysis of environmental impact assessment system in China

Environmental impact assessment (EIA) system has been established in China since 1973. In present EIA cases, there are four participants in general: governments, enterprises, EIA organizations and the public. The public has held responsible for both social costs and social duties. The public supervises social costs produced by enterprises discharging pollutant in EIA. However public participation is mostly deputized by governments, which severely weaken the independence of the public as one participant in EIA. In this paper, EIA refers to the different attitudes of the participants whose optional strategies may be described by a proper game model. According to disfigurements in EIA, three sides (governments, enterprises, and EIA organizations) dynamic iterative game theory, dynamic game theory of incomplete information, and perfect Bayesian equilibrium theory to analyze the reciprocity relation among governments, EIA organizations and enterprises. The results show that in a short period, economic benefit is preponderant over social benefit. Governments and enterprises both do not want to take EIA to reveal social costs. EIA organizations’ income comes from enterprises and the collusions are built between them to vindicate economic benefit. In a long run, social benefit loss caused by environmental pollution must be recuperated sooner or later and environmental deterioration will influence the achievements of economic benefit, so both governments and enterprises are certain to pursue high social benefit and willing to take EIA, helpful to increase private benefit. EIA organizations will make fair assessment when their economic benefit are ensured. At present, the public as silent victims can not take actual part in EIA. The EIA system must be improved to break the present equilibrium of three sides, bringing the public to the equilibrium to exert public supervision.

The Alpha-Beauty Contest: Choosing Numbers, Thinking Intervals

We present a model for the alpha-beauty contest that explains common patterns in experimental data of one-shot and iterative games. The approach is based on two basic assumptions. First, players iteratively update their recent guesses. Second, players estimate intervals rather than exact numbers to cope with incomplete knowledge of other players' choices. Under these assumptions we extend the cognitive hierarchy model of Camerer, Ho, and Chong (2003). The extended model is estimated on experimental data from a newspaper experiment.

A New Honesty for a New Game: Distinguishing Cheating from Learning in a Web-Based Testing Environment

ABSTRACT Rapid growth in the use of internet-based instructional technology (IT) necessitates greater attention to the pedagogical implications of this transition. Though much of the literature on the uses of IT focuses on outcomes and student learning, we also need to ask whether and how different technologies force us to reconceive the boundaries for both student learning and academic honesty. One IT tool, the web quiz, demands this reconception by creating the possibility for an iterative game where typically only a single-shot game had existed in the past. This change in rule structure calls for the reassessment of definitions of learning and cheating that were developed in a previous era. I review the literature on IT, student learning, and academic honesty, as well as empirical classroom data to develop a typology of behavioral responses to the web quiz environment. Specifically, I identify five behavioral options for students presented with web quiz assignments, four of which would be considered “cheating” in the traditional quiz environment. Data from the classroom confirm the existence of two of these behaviors and offer circumstantial evidence for the other three. I also test the relationship between quiz type and retention of course material to see whether web quizzes or in-class quizzes better serve student learning. I conclude with recommendations for redefining academic honesty in light of IT's alterations to the learning environment.

The ECB and the Stability Pact: policeman and judge?

The European Central Bank (ECB) has taken a forceful position in demanding that Euro-zone member states (acting collectively in the Eurogroup) maintain a strict interpretation and enforcement of the Stability Pact rules. This article challenges Artis and Winkler's (1997) use of the 'chicken game' as a model to capture the strategic interaction of the ECB with the Eurogroup with regard to the Stability Pact. It is argued that the ECB has been involved in an iterative strategic interaction with the Eurogroup, threatening to adopt 'tighter' monetary policy in order to punish fiscally wayward Eurogroup members, while for the purposes of actual monetary policy-making focusing upon its inflation target alone. The article proposes refinements in the strategic interaction to improve its analytical usefulness: the interaction involves the ECB and multiple players at once and the interaction must take into consideration the complexities of ECB monetary policy decision-making, notably the two-pillar strategy. The ECB has modified its monetary policy strategy given the potential economic and political difficulties created by the singular pursuit of Euro-zone wide monetary stability without accepting a 'lax' policy position in the iterative game.

Risk trading, network topology and banking regulation

In the context of understanding the nature of the risk transformation process of the financial system we propose an iterative risk-trading game between several agents who build their trading strategies based on a general utility setting. The game is studied numerically for different network topologies. Consequences of topology are shown for the wealth time-series of agents, for the safety and efficiency of various types of network. The proposed set-up allows an analysis of the effects of different approaches to banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find a phase-transition-like phenomenon, where the Basle parameter plays the role of temperature and system safety serves as the order parameter. This result suggests the existence of an optimal regulation parameter. As a consequence, a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, we show that banking systems with local risk-sharing cooperations have higher global default rates than systems with low cyclicality.

Banking Regulation and Network-topology Dependence of Iterative Risk-trading Games

In the context of understanding risk-regulatory behavior of financial institutions we propose a general dynamical game between several agents who pick their trading strategies depending on their individual risk-to-wealth ratio. The game is studied numerically for different network topologies. Consequences of topology are shown for the wealth time-series of agents, for the safety and efficiency of various types of networks. The model yields realistic-looking time-series of wealth and the cost of safety increases as a power-like function. The relevant model parameters should be controllable in reality. This setup allows a stringent analysis of the effects of different approaches of banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find evidence that a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, the potential impact of catastrophic events like September 11, 2001, on the financial system can be measured within this framework.

The Backward Induction Argument for the Finite Iterated Prisoner's Dilemma and the Surprise Exam Paradox

1. Consider first a loose presentation of the BIA for the FIPD. Players 1 and 2 will play a finite number of runs of a game that has the structure of a prisoner's dilemma. We assume that it is rational not to cooperate in a single-run prisoner's dilemma. But if it is rational not to cooperate in the single-run game, then it is also rational not to cooperate in the last run of the finite iterated game. Whatever your opponent chooses, the non-cooperative choice yields a higher payoff and - just like in the single-run game - there is nothing to be gained over and above the payoff in the last run. Furthermore, if there is no cooperative play to be expected in the last run, then it is also rational not to cooperate in the next to last run, since there is nothing to be gained over and above the payoff in this next to last run.

A comparative study of environmental amenity valuations

The paper reports on a comparative study of direct and indirect approaches to valuing environmental amenities (i.e., public goods), specifically, air quality in terms of its human health effects. The application of three indirect valuation methods (via market goods) is reported here: the health production method, a consumer preferences (for nonmarket goods) model, and the cost of illness method. The first and second methods are (economic) behavior-based approaches where willingness to pay for an environmental good is derived by exploiting relationships in consumption between the public good and market good(s). The third method is based on a physical relationship—a dose-response function—between the environmental good and health. The direct valuation approach encompassed three contingent valuation elicitation formats: open-ended, modified iterative bidding game, and referenda-style binary choice. The application of all four methods was based on data from a survey of a large, stratified sample of households from the Haifa metropolitan area in northern Israel. The estimates of welfare change derived by the various methods are discussed and compared.

Modified Iteration and Probability

It is always a pleasant event when apparently disparate areas of mathematics intersect: when a theorem in one discipline translates into, proves, generalizes, simplifies or explains a theorem in another. This phenomenon occurs frequently between probability theory and various aspects of classical analysis. Examples are so abundant that it is perilous even to begin a list. This note presents another such interaction. Iteration of functions produces fixed points, at least under suitable conditions. We are going to present a modification of the usual iteration procedure which has the pernicious property of retarding or even destroying the convergence to the fixed point and ascertain (purely analytically) just when this convergence is destroyed. Our modification comes about not purely by malice, but turns out to correspond to picking a non-optimal strategy in a certain iterative game of chance. The analytic criterion then reappears as an immediate corollary to an elementary pointwise convergence theorem. Here is the analytic set-up. G(w) is a strictly convex, continuously differentiable function on the interval 0 6 w 0, G(1) = 1, and 0 < G'(w) < 1 for 0 < w < 1. These conditions are more than enough to ensure that if mqnl1 = G(qn) (io = 0), then qn -* 1, the fixed point of G. Let wn be a sequence with 0 < wn < 1. Modify the in to get a sequence (n by defining 40 = 0 and

The Formation of Small Market Places in a Competitive Economic Process--The Dynamics of Agglomeration

In analyzing the city as an economic institution, it seems reasonable to ask if the advantages of proximity are sufficient to assure that traders will form and maintain a market place. This process is called agglomeration. A general theorem concerning iterative spatial games is developed first. A spatial general equilibrium model comprised of a sequence of pure trade economies is proffered. Restrictions on transport technologies sufficient to assure agglomeration are determined. The possibility of a policy maker speeding the process of agglomeration is demonstrated. In conclusion, the optimality properties of the model are discussed. The research draws heavily on the works of A. Weber [8] and G. Debreu [2]. The model includes a dynamic adjustment process which is developed from individuals' maximizing behavior.