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on Game Theory |
| By: | Catonini, Emiliano; Penta, Antonio |
| Abstract: | Backward Induction is a fundamental concept in game theory. As an algorithm, it can only be used to analyze a very narrow class of games, but its logic is also invoked, albeit informally, in several solution concepts for games with imperfect or incomplete informa-tion (Subgame Perfect Equilibrium, Sequential Equilibrium, etc.). Yet, the very meaning of ‘backward induction reasoning’ is not clear in these settings, and we lack a way to apply this simple and compelling idea to more general games. We remedy this by introducing a solution concept for games with imperfect and incomplete information, Backwards Rational-izability, that captures precisely the implications of backward induction reasoning. We show that Backwards Rationalizability satisfies several properties that are normally ascribed to backward induction reasoning, such as: (i) an incomplete-information extension of subgame consistency (continuation-game consistency); (ii) the possibility, in finite horizon games, of being computed via a tractable backwards procedure; (iii) the view of unexpected moves as mistakes; (iv) a characterization of the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis. We also discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to the backward induction logic distilled by Backwards Rationalizability, restores in dynamic games the natural comparative statics the original concept only displays in static settings. |
| Keywords: | ackward induction; backwards procedure; backwards rationalizability; incomplete information; interim perfect equilibrium, rationalizability; robustness |
| JEL: | C72 C73 D82 |
| Date: | 2022–02–03 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:126571&r= |
| By: | Itzhak Rasooly |
| Abstract: | In this paper, we design and implement an experiment aimed at testing the level-k model of auctions. We begin by asking which (simple) environments can best dis entangle the level-k model from its leading rival, Bayes-Nash equilibrium. We find two environments that are particularly suited to this purpose: an all-pay auction with uniformly distributed values, and a first-price auction with the possibility of cancelled bids. We then implement both of these environments in a virtual laboratory in order to see which theory can best explain observed bidding behaviour. We find that, when plausibly calibrated, the level-k model substantially under-predicts the observed bids and is clearly out-performed by equilibrium. Moreover, attempting to fit the level-k model to the observed data results in implausibly high estimated levels, which in turn bear no relation to the levels inferred from a game known to trigger level-k reasoning. Finally, subjects almost never appeal to iterated reasoning when asked to explain how they bid. Overall, these findings suggest that, despite its notable success in predicting behaviour in other strategic settings, the level-k model (and its close cousin cognitive hierarchy) cannot explain behaviour in auctions. |
| Date: | 2022–01–05 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:959&r= |
| By: | Sudhir A. Shah (Department of Economics, Delhi School of Economics) |
| Abstract: | The central results of this paper are dualities between actions in a decision problem that are not strongly (resp., weakly) dominated over a state space and actions that are best (resp., internal-best) replies to a state. The results admit action and state spaces that are sub-sets of abstract topological vector spaces. The generality of this setting significantly expands the set of applications of the dualities in comparison to their predecessors. This is demonstrated in the game-theoretic setting by applying the dualities to a player’s decision problem in an abstract many-player game as well as in the mixed extension of a many-player game. The formalism also allows applications beyond the game-theoretic setting, such as the characterisation of various welfare-theoretic notions of efficient outcomes in terms of the best reply properties of the outcomes. Key Words: duality, best reply, internal-best reply, strong dominance, weak dominance, efficiency JEL Codes: JC72, D81 |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:cde:cdewps:318&r= |
| By: | Surajit Borkotokey; Sujata Goala; Niharika Kakoty; Parishmita Boruah |
| Abstract: | We introduce the component-wise egalitarian Myerson value for network games. This new value being a convex combination of the Myerson value and the component-wise equal division rule is a player-based allocation rule. In network games under the cooperative framework, the Myerson value is an extreme example of marginalism, while the equal division rule signifies egalitarianism. In the proposed component-wise egalitarian Myerson value, a convexity parameter combines these two attributes and determines the degree of solidarity to the players. Here, by solidarity, we mean the mutual support or compensation among the players in a network. We provide three axiomatic characterizations of the value. Further, we propose an implementation mechanism for the component-wise egalitarian Myerson value under subgame perfect Nash equilibrium. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.02793&r= |
| By: | Daniela Di Cagno (LUISS Guido Carli); Werner Güth (Max Planck Institute for Research on Collective Goods); Tim Lohse (Berlin School of Economics and Law); Francesca Marazzi (CEIS, University of Rome "Tor Vergata"); Lorenzo Spadoni (University of Cassino and Southern Lazio) |
| Abstract: | In an ultimatum bargaining, we investigate lying as falsely stating what one privately knows without, however, excluding that others find out the truth. Specifically, we modify the Acquiring-a-Company game. Privately informed sellers send messages about the alleged value of their company to potential buyers. Via random information leaks, they can also learn the true value before proposing a price which the seller finally accepts or not. Two-thirds of all sellers exaggerate the company’s value (especially if the true value is small) but increasing the leak probability surprisingly only mildly increases truth telling. Instead, it reduces the size of the lies. Moreover, it decreases overreporting (exaggerating the value to sell at a higher price) but increases underreporting (stating values below the actual ones to increases chances of trade). Buyers who found out value misreporting anchor their price proposals on the true value but do not explicitly discriminate against liars. In contrast, sellers are fully opportunistic and make their acceptance decision mainly dependent on whether the resulting payoff is positive. Thus, morality concerns do not seem to matter much in this market exchange. Altogether probabilistic leaks enhance trade and welfare what suggests to politically facilitate and encourage e.g. whistle blowing. |
| Keywords: | Acquiring-a-company experiments, Information leaks, Cheap talk (Not) Lying, Ultimatum bargaining |
| JEL: | C78 C91 D83 D91 |
| Date: | 2022–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:531&r= |
| By: | Batabyal, Amitrajeet; Nijkamp, Peter |
| Abstract: | We study interregional competition for mobile creative capital between regions A and B. Regional authorities (RAs) in both regions use tax policy to attract the creative capital possessing members of the creative class to their region. The resulting tax revenues help RAs finance other objectives such as the provision of one or more public goods. In this setting, we accomplish five tasks. First, we explain the significance of a parameter ζ that is related to the marginal product of creative capital. Second, we compute the Nash equilibrium tax rates when each RA chooses its tax rate to maximize tax revenue. Third, we discuss how a decline in ζ affects the Nash equilibrium tax rates. Fourth, we determine the two efficient tax rates. Finally, we discuss the implications of our analysis for a policy that raises revenue by taxing creative capital. |
| Keywords: | Competition, Creative Capital, Efficiency, Mobility, Tax Revenue |
| JEL: | H20 R11 R50 |
| Date: | 2021–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:111534&r= |
| By: | David Martimort (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, EHESS - École des hautes études en sciences sociales); Jérôme Pouyet (THEMA - Théorie économique, modélisation et applications - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris Université, ESSEC Business School - Essec Business School); Thomas Trégouët (THEMA - Théorie économique, modélisation et applications - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris Université) |
| Abstract: | An incumbent seller contracts with a buyer and faces the threat of entry. The contract stipulates a price and a penalty for breach if the buyer later switches to the entrant. Sellers are heterogenous in terms of the gross surplus they provide to the buyer. The buyer is privately informed on her valuation for the incumbent's service. Asymmetric information makes the incumbent favor entry as it helps screening buyers. When the entrant has some bargaining power vis-à-vis the buyer and keeps a share of the gains from entry, the incumbent instead wants to reduce entry. The compounding effect of these two forces may lead to either excessive entry or foreclosure, and possibly to a fixed rebate for exclusivity given to all buyers. |
| Keywords: | excessive entry,foreclosure,exclusionary behavior,incomplete information |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03328387&r= |
| By: | Klaus Abbink (Monash Business School, Australia); Lu Dong (Nanjing Audit University, China); Lingbo Huang (Nanjing Audit University, China) |
| Abstract: | The rise of a new power may lead the dominant power to seek a preventive war. We study this scenario in an experimental two-stage bargaining game. In each stage, the rising power makes a bargaining offer and the declining power must choose whether to accept it or fight. Between the two stages, the winning probability shifts towards the rising power. We find fewer preventive wars when the power shift is smaller and when the rising state has the commitment power. Communication and repeated interaction decrease the likelihood of preventive wars. High fighting costs almost eliminate such wars when the rising power’s first-stage offer is sufficiently large. |
| Keywords: | power shift, commitment, bargaining, conflict, communication |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2022-01&r= |
| By: | Holden, Stein T. (Centre for Land Tenure Studies, Norwegian University of Life Sciences); Tilahun, Mesfin (Centre for Land Tenure Studies, Norwegian University of Life Sciences) |
| Abstract: | The incentivized risky investment game has become a popular tool in lab-in-the-field experiments for its simplicity and ease of comprehension compared to some of the more complex Multiple Choice List approaches that have been more commonly used in laboratory experiments. We use a field experiment to test whether the game can predict real-world investments by the same subjects based on the assumption that the game can provide a reliable measure of risk tolerance and that risk tolerance is an important predictor of investment behavior. The results show that the game cannot predict investment behavior in our sample. There are two reasons for this. First, we find substantial measurement error and low correlation when the game is repeated one year later for the same subjects. Measurement error is so large in our sample that the “obviously related instrumental variable” (ORIV) approach of Gillen, Snowberg and Yariv (2019) could not remedy the problem. Second, the game appears to suffer from low asset integration due to narrow bracketing, explaining its limited predictive power and the failure to detect attenuation bias due to measurement error. Subjects’ cognitive memory of the game played one year earlier is strongly positively related to investment intensity in the game and this result is much enhanced when correcting for the endogeneity of cognitive memory. |
| Keywords: | risky investment game; field experiment; prediction measurement error; cognitive memory; Ethiopia |
| JEL: | C93 D90 |
| Date: | 2022–02–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nlsclt:2022_005&r= |
| By: | Giulio Bottazzi; Daniele Giachini |
| Abstract: | We consider a market economy where two rational agents are able to learn the distribution of future events. In this context, we study whether moving away from the standard Bayesian belief updating, in the sense of under-reaction to some degree to new information, may be strategically convenient for traders. We show that, in equilibrium, strong under-reaction occurs, thus rational agents may strategically want to bias their learning process. Our analysis points out that the underlying mechanism driving ex-ante strategical decisions is diversity seeking. Finally, we show that, even if robust with respect to strategy selection, strong under-reaction can generate low realized welfare levels because of a long transient phase in which the agent makes poor predictions. |
| Keywords: | Learning, Strategic interaction, Behavioral Bias, Financial Markets |
| Date: | 2022–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2022/02&r= |
| By: | Victor Vikram Odouard; Michael Holton Price |
| Abstract: | Explanations for altruism, such as kin selection, reciprocity, indirect reciprocity, punishment, and genetic and cultural group selection, typically involve mechanisms that make altruists more likely to benefit from the altruism of others. Often, some form of signaling enables these mechanisms. Physical cues, for instance, help individuals recognize family members (kin selection) and others who have cooperated with them in the past (reciprocity). In the case of indirect reciprocity, where individuals cooperate with high-reputation individuals, signals help disseminate reputation information. But most accounts of indirect reciprocity take as given a truthful and misunderstanding-free communication system. In this paper, we seek to explain how such a communication system could remain evolutionarily stable in the absence of exogenous pressures. Specifically, we present three conditions that together allow signaling and cooperation to interact in a way that maintains both the effectiveness of the signal and the prevalence of cooperation. The conditions are that individuals (1) can signal about who is truthful, requiring a vital conceptual slippage between cooperation/defection and truthfulness/deceit, (2) make occasional mistakes, demonstrating how error can create stability by expressing unexpressed genes, and (3) use a "stern judging" norm that rewards defection against defectors, confirming that the norms encoded by a communication system determine its stability. |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2201.06792&r= |
| By: | Charlson, G. |
| Abstract: | We examine the effect social mistrust has on the propagation of misinformation on a social network. Agents communicate with each other and observe information sources, changing their opinion with some probability determined by their social trust, which can be low or high. Low social trust agents are less likely to be convinced out of their opinion by their peers and, in line with recent empirical literature, are more likely to observe misinformative information sources. A platform facilitates the creation of a homophilic network where users are more likely to connect with agents of the same level of social trust and the same social characteristics. Networks in which worldview is relatively important in determining network structure have more pronounced echo chambers, reducing the extent to which high and low social trust agents interact. Due to the asymmetric nature of these interactions, echo chambers then decrease the probability that agents believe misinformation. At the same time, they increase polarisation, as disagreeing agents interact less frequently, leading to a trade-off which has implications for the optimal intervention of a platform wishing to reduce misinformation. We characterise this intervention by delineating the most effective change in the platform's algorithm, which for peer-to-peer connections involves reducing the extent to which relatively isolated high and low social trust agents interact with one another. |
| Keywords: | communication, misinformation, network design, platforms |
| JEL: | D82 D83 D85 |
| Date: | 2022–01–14 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2204&r= |
| By: | Thomas R. Cook; Greg Gupton; Zach Modig; Nathan M. Palmer |
| Abstract: | Machine learning and artificial intelligence methods are often referred to as “black boxes” when compared with traditional regression-based approaches. However, both traditional and machine learning methods are concerned with modeling the joint distribution between endogenous (target) and exogenous (input) variables. Where linear models describe the fitted relationship between the target and input variables via the slope of that relationship (coefficient estimates), the same fitted relationship can be described rigorously for any machine learning model by first-differencing the partial dependence functions. Bootstrapping these first-differenced functionals provides standard errors and confidence intervals for the estimated relationships. We show that this approach replicates the point estimates of OLS coefficients and demonstrate how this generalizes to marginal relationships in machine learning and artificial intelligence models. We further discuss the relationship of partial dependence functions to Shapley value decompositions and explore how they can be used to further explain model outputs. |
| Keywords: | Machine learning; Artificial intelligence; Explainable machine learning; Shapley values; Model interpretation |
| JEL: | C14 C15 C18 |
| Date: | 2021–11–15 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedkrw:93596&r= |