Complete Information Game Research Articles

Alternating-time temporal logic with finite-memory strategies

Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In this paper we consider two other types of semantics based on finite-memory strategies. One where the memory size allowed is bounded and one where the memory size is unbounded (but must be finite). This is motivated by the high complexity of model-checking with perfect recall semantics and the severe limitations of memoryless strategies. We show that both types of semantics introduced are different from perfect recall and memoryless semantics and next focus on the decidability and complexity of model-checking in both complete and incomplete information games for ATL/ATL*. In particular, we show that the complexity of model-checking with bounded-memory semantics is Delta_2p-complete for ATL and PSPACE-complete for ATL* in incomplete information games just as in the memoryless case. We also present a proof that ATL and ATL* model-checking is undecidable for n >= 3 players with finite-memory semantics in incomplete information games.

Implementability of correlated and communication equilibrium outcomes in incomplete information games

In a correlated equilibrium, the players’ choice of actions is directed by correlated random messages received from an outside source, or mechanism. These messages allow for more equilibrium outcomes than without any messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also reflect the types of the players, either because they are affected by extraneous factors that also affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Mechanisms may be further differentiated by the connections between the messages that the players receive and their own and the other players’ types, by whether the messages are statistically dependent or independent, and by whether they are random or deterministic. Consequently, whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the corresponding number is 14 or 15 for correlated equilibria and even larger—15, 16 or 17—for communication equilibria. For both solution concepts, the implication relations between the different kinds of equilibria form a two-dimensional lattice, which is considerably more intricate than the single-dimensional one of the complete information case.

Auctions for social lending: A theoretical analysis

Prosper, today the second largest social lending marketplace with nearly 1.5 million members and $380 million in funded loans, employed an auction mechanism amongst lenders to finance each borrower's loan until 2010. Given that a basic premise of social lending is cheap loans for borrowers, how does the Prosper auction do in terms of the borrower's payment, when lenders are strategic agents with private true interest rates? We first analyze the Prosper auction as a game of complete information and fully characterize its Nash equilibria, and show that the uniform-price Prosper mechanism, while simple, can lead to much larger payments for the borrower than the VCG mechanism. We next compare the Prosper mechanism against the borrower-optimal auction in an incomplete information setting, and conclude by examining the Prosper mechanism when modeled as a dynamic auction, and provide tight bounds on the price for a general class of bidding strategies.

A Note on Purification Theorem

The purification Theorem of Harsanyi (1973) argues that one can understand the mixed strategy Nash equilibrium of a simultaneous move complete information game as the limit of a particular Bayesian Nash equilibrium of the incomplete information version of the same game where the players choose pure strategies and the incompleteness of information almost vanishes. This paper analyzes an incomplete information coordination game and the purification of the pure strategy Bayesian Nash equilibrium (as stipulated by Harsanyi (1973)). Through comparative static analysis, the paper shows that besides inheriting the problematic feature of the mixed strategy equilibrium of the complete information game, the incomplete information game also has new problematic feature of its own.

A detail-free mediator

We present a cheap talk extension to any two-player, finite, complete information game, and ask what correlations over actions are implementable in Nash equilibria of the extended game. In the extension, players communicate repeatedly through a detail-free mediator that has been studied in Lehrer (1991) and in Gossner and Vieille (2001). The extension captures situations in which people can observe the opponentʼs face during the conversation. While Gossner and Vieille (2001) prove that no correlation can be securely implemented by using only this mediator, we prove a result closer to Lehrer (1991), namely, that the Nash equilibrium payoffs of the extended game essentially coincide with the correlated equilibrium payoffs of the underlying game. The contrasting results can be explained with our additional assumptions that the players can also communicate directly and, more importantly, the private messages sent to the mediator can be recorded and revealed later in the conversation.

Noise-independent selection in multidimensional global games

Abstract This paper examines many-player many-action global games with multidimensional state parameters. It establishes that the notion of noise-independent selection introduced by Frankel, Morris and Pauzner [D. Frankel, S. Morris, A. Pauzner, Equilibrium selection in global games with strategic complementarities, J. Econ. Theory 108 (2003) 1–44] for one-dimensional global games is robust when the setting is extended to the one proposed by Carlsson and Van Damme [H. Carlsson, E. Van Damme, Global games and Equilibrium selection, Econometrica 61 (1993) 989–1018]. More precisely, our main result states that if an action profile of some complete information game is noise-independently selected in one-dimensional global games, then it is also noise-independently selected in all multidimensional global games.

Non-Cooperative Location Privacy

In mobile networks, authentication is a required primitive for most security protocols. Unfortunately, an adversary can monitor pseudonyms used for authentication to track the location of mobile nodes. A frequently proposed solution to protect location privacy suggests that mobile nodes collectively change their pseudonyms in regions called mix zones. This approach is costly. Self-interested mobile nodes might, thus, decide not to cooperate and jeopardize the achievable location privacy. In this paper, we analyze non-cooperative behavior of mobile nodes by using a game-theoretic model, where each player aims at maximizing its location privacy at a minimum cost. We obtain Nash equilibria in static n-player complete information games. As in practice mobile nodes do not know their opponents' payoffs, we then consider static incomplete information games. We establish that symmetric Bayesian-Nash equilibria exist with simple threshold strategies. By means of numerical results, we predict behavior of selfish mobile nodes. We then investigate dynamic games where players decide to change their pseudonym one after the other and show how this affects strategies at equilibrium. Finally, we design protocols-PseudoGame protocols-based on the results of our analysis and simulate their performance in vehicular network scenarios.

QME special issue on discrete games

I am pleased and excited to present this special issue of Quantitative Marketing and Economics on discrete games. We have collected together four excellent papers dealing with issues related to this important topic that lies at the intersection of marketing and economics. Two of the papers in the special issue deal with Bayesian estimation of discrete games, with Narayanan focusing on games of complete information and Misra focusing on games of incomplete information. The other two papers deal with applications of interest to marketers. The paper by Orhun investigates the geographic positioning of supermarkets in the presence of both complete (perfect) and incomplete (imperfect) information, and demonstrates the importance of allowing for location-specific complete information. The paper by Data and Sudhir examines the influence of zoning restrictions on store entry, location and format choices. Special thanks go to Sanjog Misra for his help in organizing and soliciting papers for this special issue. We hope you enjoy the papers and find this issue of QME to be a useful resource in your own research. Quant Mark Econ (2013) 11:1 DOI 10.1007/s11129-013-9134-2

Modeling a Married Couple’s Reciprocal Relationship

A model was developed and a static game of complete information was applied in an examination of a married couple’s reciprocal relationship. Each chose best strategies (i.e., optimal responses) to maximize payoffs (i.e., happiness). Theoretical analysis suggests that the couple’s happiness is endogenously and positively correlated and simultaneously determined. If the wife (or the husband) is not happy with the relationship, it is impossible for the husband (or the wife) to be happy with the relationship.

The health queuing game

This paper studies agent-to-agent games in competition for a free public resource. The resource is not evidently scarce, scarcity may, however, be the equi- librium outcome. The agents' attributes may dier as well as quality parameters between dierent public resources. The examples are taken from the health sector. Based on simple two-player simultaneous games of complete information, results re- garding agent equilibrium quality choices are derived. Most notably, Nash equilibria of the type: very ill patients choose low quality hospitals (denoted adverse patient allocation in the paper) are demonstrated. Furthermore, it is argued that a situation characterized by patients with relatively mild diseases but large patient variability (big dierences between patients regarding the given disease) and a health system with medium competition are prime candidates for Nash equilibria characterized by such Adverse patient allocation eects.

Bayesian estimation of discrete games of complete information

Bayesian estimation of discrete games of complete information

Econometric Analysis of Games with Multiple Equilibria

This article reviews the recent literature on the econometric analysis of games in which multiple solutions are possible. Multiplicity does not necessarily preclude the estimation of a particular model (and, in certain cases, even improves its identification), but ignoring it can lead to misspecifications. The review starts with a general characterization of structural models that highlights how multiplicity affects the classical paradigm. Because the information structure is an important guide to identification and estimation strategies, I discuss games of complete and incomplete information separately. Although many of the techniques discussed here can be transported across different information environments, some are specific to particular models. Models of social interactions are also surveyed. I close with a brief discussion of postestimation issues and research prospects.

Correlated equilibrium and higher order beliefs about play

We study a refinement of correlated equilibrium in which playersʼ actions are driven by their beliefs and higher order beliefs about the play of the game (beliefs over what other players will do, over what other players believe others will do, etc.). For any finite, complete-information game, we characterize the behavioral implications of this refinement with and without a common prior, and up to any a priori fixed depth of reasoning. In every finite game “most” correlated equilibrium distributions are consistent with this refinement; as a consequence, this refinement gives a classification of “most” correlated equilibrium distributions based on the maximum order of beliefs used by players in the equilibrium. On the other hand, in a generic two-player game any non-degenerate mixed-strategy Nash equilibrium is not consistent with this refinement.

Equilibrium selection in static and dynamic entry games

We experimentally assess the predictive power of two equilibrium selection principles for binary N-player entry games with strategic complementarities. In static entry games, we test the theory of global games which posits that players play games of complete information as if they were playing a related global game of incomplete information. By contrast, in dynamic n-period entry games, the efficient subgame perfect equilibrium prediction is for all to enter whenever the payoff relevant state variable exceeds a certain threshold. The subgame perfect entry threshold of the dynamic game will generally differ from the global game threshold of the static version of the same game. Nevertheless, our experimental findings suggest that entry thresholds are similar between static and dynamic versions of the same game. An implication is that the modeling of entry games with strategic complementarities as static, one-shot games – ignoring the dynamic element of such interactions – may not be unreasonable.

A Study on Feasibility of Upstream and Downstream Ecological Cooperation - An Example of Game Among Upstream and Downstream Villages

The feasibility of area ecological cooperation without government interaction, and the possibility of building up effective ecological cooperation mechanism are the main questions need to be studied for ecological construction and area harmonious development. This article used the game among upstream and downstream villages as an example, analyzed upstream and downstream village under static game of complete information, single stage game and repeated game model, and stated that the sanction among upstream and downstream ecological cooperation is very low without government interaction, however, this result can be remodeled at certain degree through changing the rules of the game and payoff matrix of both game side.

Clustering routing algorithm of wireless sensor networks based on Bayesian game

To avoid uneven energy consuming in wireless sensor networks, a clustering routing model is proposed based on a Bayesian game. In the model, Harsanyi transformation is introduced to convert a static game of incomplete information to the static game of complete but imperfect information. In addition, the existence of Bayesian nash equilibrium is proved. A clustering routing algorithm is also designed according to the proposed model, both cluster head distribution and residual energy are considered in the design of the algorithm. Simulation results show that the algorithm can balance network load, save energy and prolong network lifetime effectively.

A SMUGGLING GAME WITH THE SECRECY OF SMUGGLER'S INFORMATION

This paper deals with a smuggling game with multiple stages, in which Customs and a smuggler participate. Customs and the smuggler are allowed to take an action of patrol and smuggling, respectively, within the limited number of chances. Customs obtains reward by the capture of the smuggler and the smuggler gets reward by the success of smuggling. The reward or the payoff of the game is brought at each stage and is assumed to be zero-sum. Almost all past researches modeled their games by the so- called complete information game and they assumed that each player knows the past strategies taken by his opponent or never knows them. Recently, we recognize that information is crucial to the results of the games. In this paper, we deal with a smuggling game with incomplete information, where information acquisition is asymmetric between players and is disadvantageous to Customs, and we evaluate the value of information by developing a computational methodology to derive Bayesian equilibrium.

Structural Workshop Paper—Estimating Discrete Games

This paper provides a critical review of the methods for estimating static discrete games and their relevance for quantitative marketing. We discuss the various modeling approaches, alternative assumptions, and relevant trade-offs involved in taking these empirical methods to data. We consider games of both complete and incomplete information, examine the primary methods for dealing with the coherency problems introduced by multiplicity of equilibria, and provide concrete examples from the literature. We illustrate the mechanics of estimation using a real-world example and provide the computer code and data set with which to replicate our results.

Walking the talk in multiparty bargaining: An experimental investigation

We study the framing effects of communication on payoffs in multiparty bargaining. Communication has been shown to be more truthful and revealing than predicted in equilibrium. Because talk is preference-revealing, it may effectively frame bargaining around a logic of fairness or competition, moving parties on a path toward or away from equal-division agreements. These endogenous framing effects may outweigh any overall social utility effects due to the mere presence of communication. In two studies, we find that non-binding talk about fairness within a three-party, complete-information game leads toward off-equilibrium, equal division payoffs, while non-binding talk focusing on Competitive Reasoning moves parties away from equal divisions. Our two studies allow us to demonstrate that manipulated pre-game talk and spontaneous within-game dialogue lead to the same results.

Strategic substitutes or complements? The game of where to fish

The “global game with strategic substitutes and complements” of Karp et al. (2007) is used to model the decision of where to fish. A complete information game is assumed, but the model is generalized to S>1 sites. In this game, a fisherman’s payoff depends on fish density in each site and the actions of other fishermen which can lead to congestion or agglomeration effects. Stable and unstable equilibria are characterized, as well as notions of equilibrium dominance. The model is applied to the Alaskan flatfish fishery by specifying a strategic interaction function (response to congestion) that is a non-linear function of the degree of congestion present in a given site. Results suggest that the interaction function may be non-monotonic in congestion.