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on Game Theory |
| By: | Fabian R. Pieroth; Martin Bichler |
| Abstract: | Game theory largely rests on the availability of cardinal utility functions. In contrast, only ordinal preferences are elicited in fields such as matching under preferences. The literature focuses on mechanisms with simple dominant strategies. However, many real-world applications do not have dominant strategies, so intensities between preferences matter when participants determine their strategies. Even though precise information about cardinal utilities is unavailable, some data about the likelihood of utility functions is typically accessible. We propose to use Bayesian games to formalize uncertainty about decision-makers utilities by viewing them as a collection of normal-form games where uncertainty about types persist in all game stages. Instead of searching for the Bayes-Nash equilibrium, we consider the question of how uncertainty in utilities is reflected in uncertainty of strategic play. We introduce $\alpha$-Rank-collections as a solution concept that extends $\alpha$-Rank, a new solution concept for normal-form games, to Bayesian games. This allows us to analyze the strategic play in, for example, (non-strategyproof) matching markets, for which we do not have appropriate solution concepts so far. $\alpha$-Rank-collections characterize a range of strategy-profiles emerging from replicator dynamics of the game rather than equilibrium point. We prove that $\alpha$-Rank-collections are invariant to positive affine transformations, and that they are efficient to approximate. An instance of the Boston mechanism is used to illustrate the new solution concept. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.10317&r=gth |
| By: | Chatterji, Shurojit (Singapore Management University); Kunimoto, Takashi (Singapore Management University); Ramos, Paulo (Singapore Management University) |
| Abstract: | A social choice function (SCF) is said to be Nash implementable if there exists a mechanism in which every Nash equilibrium outcome coincides with that specified by the SCF. The main objective of this paper is to assess the impact of considering mixed strategy equilibria in Nash implementation. To do this, we focus on environments with two agents and restrict attention to finite mechanisms. We call a mixed strategy equilibrium “compelling” if its outcome Pareto dominates any pure strategy equilibrium outcome. We show that if the finite environment and the SCF to be implemented jointly satisfy what we call Condition P+M, we construct a finite mechanism which Nash implements the SCF in pure strategies and possesses no compelling mixed strategy equilibria. This means that the mechanism might possess mixed strategy equilibria which are “not” compelling. Our mechanism has several desirable features: transfers can be completely dispensable; only finite mechanisms are considered; integer games are not invoked; and players’ attitudes toward risk do not matter. |
| Keywords: | implementation; compelling equilibria; ordinality; mixed strategies[Nash equilibrium |
| JEL: | C72 D78 D82 |
| Date: | 2022–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2022_010&r=gth |
| By: | Bhattacherjee, Sanjay; Chakravarty, Satya R.; Sarkar, Palash |
| Abstract: | This article introduces a general model for voting games with multiple weight vectors. Each weight vector characterises a parameter representing a distinct aspect of the voting mechanism. Our main innovation is to model the winning condition by an arbitrary dichotomous function which determines whether a coalition is winning based on the weights that the coalition has for the different parameters. Previously studied multi-parameter games are obtained as particular cases of the general model. We identify a new and interesting class of games, that we call hyperplane voting games, which are compactly expressible in the new model, but not necessarily so in the previous models. For the general model of voting games that we introduce, we describe dynamic programming algorithms for determining various quantities required for computing different voting power indices. Specialising to the known classes of multi-parameter games, our algorithms provide unified and simpler alternatives to previously proposed algorithms. |
| Keywords: | weighted majority voting game, multi-parameter games, Boolean formula, voting power, dynamic programming |
| JEL: | C71 |
| Date: | 2022–11–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115407&r=gth |
| By: | Hitoshi Matsushima (Department of Economics, University of Tokyo) |
| Abstract: | We investigate the implementation of social choice functions with asymmetric information concerning the state from an epistemological perspective. Although agents are either selfish or honest, they do not expect other participants to be honest. However, an honest agent may exist not among participants but in their higher-order beliefs. We assume that “all agents are selfish†never happens to be common knowledge. We show a positive result in general asymmetric information environments, demonstrating that with a minor restriction on signal correlation called information diversity, any incentive-compatible social choice function, whether ethical or nonethical, is uniquely implementable in the Bayesian Nash equilibrium. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf548&r=gth |
| By: | Garfinkel, Michelle (University of California, Irvine); Syropoulos, Constantinos (Drexel University) |
| Abstract: | We consider a dynamic setting in which two sovereign states with overlapping ownership claims on a resource/asset first arm and then choose whether to resolve their dispute violently through war or peacefully through settlement. Both approaches depend on the states’ military capacities, but have very different outcomes. War precludes the possibility of international trade and can be destructive; however, once a winner is declared, arming is unnecessary in future periods. By contrast, a peaceful resolution avoids destruction and supports mutually advantageous trade; yet, settlements must be renegotiated in the shadow of arming and the threat of war. In this setting, we characterize the conditions under which peace arises as a stable equilibrium over time. We find that, depending on the destructiveness of war, time preferences, and the initial distribution of resource endowments, greater gains from trade can reduce arming and pacify international tensions. Even when the gains from trade are relatively small, peace might be sustainable, but only for more uneven endowment distributions. |
| Keywords: | Interstate war; armed peace; unarmed peace; security policies; gains from trade; shadow of the future. |
| JEL: | C72 C78 D30 D70 D74 F10 F51 F60 |
| Date: | 2022–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:ris:drxlwp:2022_009&r=gth |
| By: | Chowdhury Mohammad Sakib Anwar; Alexander Matros; Sonali SenGupta |
| Abstract: | We present a model of public good provision with a distributor. Our main result describes a symmetric mixed-strategy equilibrium, where all agents contribute to a common fund with probability $p$ and the distributor provides either a particular amount of public goods or nothing. A corollary of this finding is the efficient public good provision equilibrium where all agents contribute to the common fund, all agents are expected to contribute, and the distributor spends the entire common fund for the public good provision. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.10642&r=gth |
| By: | Marina Emiris (: Economics and Research Department, National Bank of Belgium); François Koulischer (University of Luxembourg); Christophe Spaenjers (Leeds School of Business, University of Colorado Boulder) |
| Abstract: | We model mortgage refinancing as a bargaining game involving the borrowing household, the incumbent lender, and an outside bank. In equilibrium, the borrower’s ability to refinance depends both on the competitiveness of the local banking market and on the cost of switching banks. We find empirical support for the key predictions of our model using a unique data set containing the population of mortgages in Belgium. In particular, households’ refinancing propensities are positively correlated with the number of local branches and negatively correlated with local mortgage market concentration. Moreover, households are more likely to refinance externally if they already have a relation with more than one bank, but the effect is mitigated if their current mortgage lender has a branch locally. |
| Keywords: | mortgage markets; refinancing; bargaining; bank competition; switching costs |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbb:reswpp:202210-422&r=gth |
| By: | Marco de Pinto; Laszlo Goerke; Alberto Palermo |
| Abstract: | We consider a principal-agent relationship with adverse selection. Principals pay informational rents due to asymmetric information and sell their output in a homogeneous Cournot-oligopoly. We find that asymmetric information may mitigate or more than compensate the welfare reducing impact of market power, irrespective of whether the number of firms is given exogenously or determined endogenously by a profit constraint. We further show that welfare in a setting with adverse selection may be higher than the maximized welfare level attainable in a world with perfect observability. |
| Keywords: | adverse selection, oligopoly, welfare |
| JEL: | D43 D82 L51 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10003&r=gth |
| By: | Rosato, Antonio; Tymula, Agnieszka |
| Abstract: | We present experimental evidence on bidding in second-price auctions with real objects. Our novel design, combining a second-price auction with an individual-specific binary choice task based on the outcome of the auction, allows us to directly identify over and under-bidding. We analyze bidding in real-object and induced-value auctions, and find significant deviations from truthful bidding in both. Overall, under-bidding is somewhat more prevalent than over-bidding; yet, the latter has a bigger magnitude, especially with induced values. At the individual level, we find no relation between the tendency to deviate from truthful bidding in induced-value vs. real-object auctions. |
| Keywords: | Second-price Auctions; Overbidding; Consumer Surplus. |
| JEL: | D44 D81 D91 D92 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115427&r=gth |
| By: | Lau, C. Oscar |
| Abstract: | Travel circle is a metaphor for supply chains: in travel circle, travelers are transported by carriers in multiple legs from the center to diverse destinations on the circumference; in supply chains, goods are transformed in multiple stages by firms from natural resources into differentiated products. The model is generated using only three cost parameters. At the start of supply chains, a few firms mass-produce standardized commodities at low unit costs; at the end, many firms produce distinctive products in small scales at high unit costs. As an extension, the circle’s size is endogenized to account for consumers’ preferences for varieties. |
| Keywords: | Product differentiation, Scale economies, Entry game |
| JEL: | L11 L13 L23 L25 |
| Date: | 2022–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115291&r=gth |
| By: | Jean-Marc Bourgeon; José De Sousa; Alexis Noir-Luhalwe |
| Abstract: | We examine the risky choices of pairs of contestants in a popular radio game show in France. At one point during the COVID-19 pandemic the show, held in person, had to switch to an all-remote format. We find that such an exogenous change in social context affected risk-taking behavior. Remotely, pairs take far fewer risks when the stakes are high than in the flesh. This behavioral difference is consistent with prosocial behavior theories, which argue that the nature of social interactions influences risky choices. Our results suggest that working from home may reduce participation in profitable but risky team projects. |
| Keywords: | COVID-19, social distancing, social pressure, decision making, risk |
| JEL: | C93 D81 D91 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10063&r=gth |
| By: | Marie-Laure Cabon-Dhersin (LERN - Laboratoire d'Economie Rouen Normandie - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - IRIHS - Institut de Recherche Interdisciplinaire Homme et Société - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université) |
| Abstract: | We revisit the classic comparison of Bertrand and Cournot competition by studying how the form of competition between shipping companies affects transport prices, international trade, consumer and producer surplus, and social welfare in two countries that coordinate their environmental policies. We show that the standard Bertrand-Cournot ranking only prevails when pollution abatement technologies are sufficiently efficient. |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03822627&r=gth |