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on Game Theory |
| By: | Jason Milionis; Christos Papadimitriou; Georgios Piliouras; Kelly Spendlove |
| Abstract: | Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile is mapped to the next, this becomes a problem in the theory of dynamical systems. We apply this theory, and in particular the concepts of chain recurrence, attractors, and Conley index, to prove a general impossibility result: there exist games for which any dynamics is bound to have starting points that do not end up at a Nash equilibrium. We also prove a stronger result for $\epsilon$-approximate Nash equilibria: there are games such that no game dynamics can converge (in an appropriate sense) to $\epsilon$-Nash equilibria, and in fact the set of such games has positive measure. Further numerical results demonstrate that this holds for any $\epsilon$ between zero and $0.09$. Our results establish that, although the notions of Nash equilibria (and its computation-inspired approximations) are universally applicable in all games, they are also fundamentally incomplete as predictors of long term behavior, regardless of the choice of dynamics. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.14129&r= |
| By: | Besner, Manfred |
| Abstract: | If a player boycotts another player, it means that the cooperation gains of all coalitions containing both players vanish. In the associated coalition function, both players are now disjointly productive with respect to each other. The disjointly productive players property states that a player's payoff does not change when another player who is disjointly productive to that player is removed from the game. We show that the Shapley value is the only TU-value that satisfies efficiency and the disjointly productive players property and for which the impact of a boycott is the same for the boycotting and the boycotted player. Analogous considerations are made for the proportional Shapley value and the class of (positively) weighted Shapley values. |
| Keywords: | Cooperative game · (Weighted/proportional) Shapley value · Disjointly productive players · (Weighted/proportional) impacts of boycotts |
| JEL: | C7 C71 |
| Date: | 2022–04–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112620&r= |
| By: | Denizalp Goktas; Jiayi Zhao; Amy Greenwald |
| Abstract: | The behavior of no-regret learning algorithms is well understood in two-player min-max (i.e, zero-sum) games. In this paper, we investigate the behavior of no-regret learning in min-max games with dependent strategy sets, where the strategy of the first player constrains the behavior of the second. Such games are best understood as sequential, i.e., min-max Stackelberg, games. We consider two settings, one in which only the first player chooses their actions using a no-regret algorithm while the second player best responds, and one in which both players use no-regret algorithms. For the former case, we show that no-regret dynamics converge to a Stackelberg equilibrium. For the latter case, we introduce a new type of regret, which we call Lagrangian regret, and show that if both players minimize their Lagrangian regrets, then play converges to a Stackelberg equilibrium. We then observe that online mirror descent (OMD) dynamics in these two settings correspond respectively to a known nested (i.e., sequential) gradient descent-ascent (GDA) algorithm and a new simultaneous GDA-like algorithm, thereby establishing convergence of these algorithms to Stackelberg equilibrium. Finally, we analyze the robustness of OMD dynamics to perturbations by investigating online min-max Stackelberg games. We prove that OMD dynamics are robust for a large class of online min-max games with independent strategy sets. In the dependent case, we demonstrate the robustness of OMD dynamics experimentally by simulating them in online Fisher markets, a canonical example of a min-max Stackelberg game with dependent strategy sets. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.14126&r= |
| By: | Martin Peitz; Lily Samkharadze |
| Abstract: | Platform competition can be intense when offering non-differentiated services. However, competition is somewhat relaxed if platforms cannot set negative prices. If platforms collude they may be able to implement the outcome that maximizes industry profits. In an infinitely repeated game with perfect monitoring, this is feasible if the discount factor is sufficiently large. When this is not possible, under some condition, a collusive outcome with one-sided rent extraction along the equilibrium path can be sustained that leads to higher profits than the non-cooperative outcome. |
| Keywords: | Two-sided markets, tacit collusion, cartelization, price structure, platform competition |
| JEL: | L41 L13 D43 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_331v2&r= |
| By: | Syngjoo Choi; Sanjeev Goyal; Frédéric Moisan (Division of Social Science) |
| Abstract: | We consider a setting in which individuals can purchase information at a cost and form costly links to access information purchased by others. The theory predicts that in every equilibrium of this game the network is a `star'. For small groups, there exists a unique purchase configuration -a pure influencer outcome, in which the hub node purchases information while all others free ride. For large groups, there exists, in addition, a pure connector outcome in which the hub purchases no information and the peripheral players purchase information. We test these predictions on a new experimental platform with asynchronous activity in continuous time. We start with a baseline setting where subjects only see their own payoffs. We find that subjects create a star network. In small groups, the hub purchases equilibrium level information, but in large groups the hub purchases excessive information and as a result earns low payoffs. To study the reasons for this excessive investment we propose a treatment in which subjects see everyone's payoffs. We find that in small groups the pure influencer out- come obtains but that in large groups the pure-connector outcome now becomes common, suggesting that information and group size interact in powerful ways to shape networks and payoffs. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:nad:wpaper:20220077&r= |
| By: | Justus Haucap; Christina Heldman; Holger A. Rau |
| Abstract: | Many cartels are formed by individual managers of different firms, but not by firms as collectives. However, most of the literature in industrial economics neglects individuals’ incentives to form cartels. Although oligopoly experiments reveal important insights on individuals acting as firms, they largely ignore individual heterogeneity, such as gender differences. We experimentally analyze gender differences in prisoner’s dilemmas, where collusive behavior harms a passive third party. In a control treatment, no externality exists. To study the influence of social distance, we compare subjects’ collusive behaviour in a within-subjects setting. In the first game, subjects have no information on other players, whereas they are informed about personal characteristics in the second game. Results show that guilt-averse women are significantly less inclined to collude than men when collusion harms a third party. No gender difference can be found in the absence of a negative externality. Interestingly, we find that women are not sensitive to the decision context, i.e., even when social distance is small they hardly behave collusively when collusion harms a third party. |
| Keywords: | collusion, cartels, competition policy, antitrust, gender differences |
| JEL: | C92 D01 D43 J16 K21 L13 L41 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9614&r= |
| By: | Wang Zhijian |
| Abstract: | Game dynamics structure (e.g., endogenous cycle motion) in human subjects game experiments can be predicted by game dynamics theory. However, whether the structure can be controlled by mechanism design to a desired goal is not known. Here, using the pole assignment approach in modern control theory, we demonstrate how to control the structure in two steps: (1) Illustrate an theoretical workflow on how to design a state-depended feedback controller for desired structure; (2) Evaluate the controller by laboratory human subject game experiments and by agent-based evolutionary dynamics simulation. To our knowledge, this is the first realisation of the control of the human social game dynamics structure in theory and experiment. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.06088&r= |
| By: | Tongseok Lim |
| Abstract: | The fundamental connection between stochastic differential equations (SDEs) and partial differential equations (PDEs) has found numerous applications in diverse fields. We explore a similar link between stochastic calculus and combinatorial PDEs on graphs with Hodge structure, by showing that the solution to the Hodge-theoretic Poisson's equation on graphs allows for a stochastic integral representation driven by a canonical time-reversible Markov chain. When the underlying graph has a hypercube structure, we further show that the solution to the Poisson's equation can be fully characterized by five properties, which can be thought of as a completion of the Lloyd Shapley's four axioms. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.06860&r= |
| By: | Bastien Baldacci; Philippe Bergault; Dylan Possama\"i |
| Abstract: | We design a market-making model \`a la Avellaneda-Stoikov in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers' behaviour, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB--Fokker--Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviours for the market-takers and takes into account the impact of their strategies on the price process. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.13053&r= |
| By: | Yevhen Havrylenko; Maria Hinken; Rudi Zagst |
| Abstract: | Equity-linked insurance products often have capital guarantees. Common investment strategies ensuring these guarantees are challenged nowadays by low interest rates. Thus, we study an alternative strategy when an insurance company shares financial risk with a reinsurance company. We model this situation as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the utilities of both parties. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.04053&r= |
| By: | Itai Arieli; Yakov Babichenko; Fedor Sandomirskiy |
| Abstract: | A sender communicates with a receiver through a sequence of mediators. The sender is the only informed agent and the receiver is the only one taking an action. All the agents have their own utility functions, which depend on the receiver's action and the state. For any number of mediators, the sender's optimal value is characterized. For one mediator, the characterization has a clear geometric meaning of constrained concavification of the sender's utility, optimal persuasion requires the same number of signals as without mediators, and the presence of the mediator is never profitable for the sender. Surprisingly, the second mediator may improve the sender's utility; however, optimal persuasion with several mediators may require more signals. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.04285&r= |
| By: | Chapkovski, Philipp |
| Abstract: | Using the results of a large-scale (N=900) online experiment, this paper investigates how the information about a group corruption level may harm intergroup relations. Corruption indices are widely used as a measure of quality of governance. But in addition to be a valuable tool for investors and policy makers for making informed decisions, they may also result in statistical discrimination: people from a more ‘corrupt’ region may be perceived as less trustworthy or more inclined to dishonest behavior. We manipulated the amount of information people have about three different Russian regions in two simple behavioral games (‘Cheating game’ and Trust game). In a Cheating game after the main stage where they report whether they observed a head or a tail on a flipped coin, they guessed how many participants in each of the three regions reported more personally profitable outcome (heads) as well as make trasfer decisions in a standard trust game. In the baseline treatment we provided them with a set of generic information about each region (such as population size), while in the main treatment they were additionally informed about the degree of perceived corruption in each region. The presence of corruption information made people substantially overestimate the degree of dishonesty in more ‘corrupt’ regions and decreased the trust towards a person from this region. The results demonstrate the potentially harmful unintended consequences of corruption indices that have to be taken into account by policy makers. |
| Keywords: | Corruption; experiments; online research; survey research |
| JEL: | C90 C92 D73 Z13 |
| Date: | 2022–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112598&r= |
| By: | Hanappi, Hardy |
| Abstract: | This paper presents an interpretation of the underlying dynamics of global political economy, which has led to the invasion of Ukraine by Russia in February 2022. It thus is an alternative to interpretations that view the individual psychological traits of Vladimir Putin as the driving force behind this event. To enable a more sensible account, it turns out to be necessary to go back in the history of the conflict between Russia and NATO to the times of the Cold War. Briefly, two important fields of methodology – a theory of power and game theory – have to be touched upon. Finally, the justified emotional disgust concerning Putin’s aggressive war and the somewhat more detached scientific analysis are tried to be reconciled in the concluding paragraphs. |
| Keywords: | Russia, Ukraine, Political Economy, War, Game Theory |
| JEL: | C73 F5 F51 F52 F54 |
| Date: | 2022–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112394&r= |
| By: | Alexander Kolesnikov; Fedor Sandomirskiy; Aleh Tsyvinski; Alexander P. Zimin |
| Abstract: | We consider the problem of revenue-maximizing Bayesian auction design with several i.i.d. bidders and several items. We show that the auction-design problem can be reduced to the problem of continuous optimal transportation introduced by Beckmann. We establish the strong duality between the two problems and demonstrate the existence of solutions. We then develop a new numerical approximation scheme that combines multi-to-single-agent reduction and the majorization theory insights to characterize the solution. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.06837&r= |
| By: | Abhijit Banerjee; Olivier Compte |
| Abstract: | We explore a model of non-Bayesian information aggregation in networks. Agents non-cooperatively choose among Friedkin-Johnsen type aggregation rules to maximize payoffs. The DeGroot rule is chosen in equilibrium if and only if there is noiseless information transmission...leading to consensus. With noisy transmission, while some disagreement is inevitable, the optimal choice of rule blows up disagreement: even with little noise, individuals place substantial weight on their own initial opinion in every period, which inflates the disagreement. We use this framework to think about equilibrium versus socially efficient choice of rules and its connection to polarization of opinions across groups. |
| JEL: | D0 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:29897&r= |
| By: | Raphael Corbi; Fabio Miessi Sanches |
| Abstract: | This paper examines how religious subsidies contributed to the rise of Evangelicals and the decline of the Catholic church, a commonly observed trend in the Christian world. Using the Brazilian experience as a showcase, we build and estimate a dynamic game of church entry using temple entry/exit data across municipalities for 1991-2018. Our counterfactual analysis shows that Evangelicals gain market share from Catholics as tax exemptions increase entry of smaller churches. By combining DiD estimates and our counterfactual scenario, we show that the vote share of the Congressional Evangelical caucus would have been 20% lower if state subsidies had been removed. |
| Keywords: | Religion; Tax; Dynamic Oligopoly; Dynamic Game Estimation |
| JEL: | Z12 H25 C57 C73 |
| Date: | 2022–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:spa:wpaper:2022wpecon09&r= |
| By: | Noga Alon; Benjamin Gunby; Xiaoyu He; Eran Shmaya; Eilon Solan |
| Abstract: | A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached because some player deviates, then an outside observer can identify the deviator. We also construct identification methods in two nontrivial cases. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.03744&r= |
| By: | Gregorio Curello; Ludvig Sinander |
| Abstract: | In the canonical persuasion model, comparative statics has been an open question. We answer it, delineating which shifts of the sender's interim payoff lead her optimally to choose a more informative signal. Our first theorem identifies an ordinal notion of 'increased convexity' that we show characterises those shifts of the sender's interim payoff that lead her optimally to choose no less informative signals. To strengthen this conclusion to 'more informative' requires further assumptions: our second theorem identifies the necessary and sufficient condition on the sender's interim payoff, which strictly generalises the 'S'-shape commonly imposed in the literature. (Note: preliminary and incomplete.) |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.07474&r= |
| By: | Zhijian Wang; Shujie Zhou; Qinmei Yao; Yijia; Wang |
| Abstract: | Game dynamics theory, as a field of science, the consistency of theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is the presentation. However, the merging works have not got rid of the constraints of Euclidean two-dimensional cycle so far. This paper uses a classic four-strategy game to study the dynamic structure (non-Euclidean superplane cycle). The consistency is in significant between the three ways: (1) the analytical results from evolutionary dynamics equations, (2) agent-based simulation results from learning models and (3) laboratory results from human subjects game experiments. The consistency suggests that, game dynamic structure could be quantitatively predictable, observable and controllable in general. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.14669&r= |
| By: | Saeed Alaei; Ali Makhdoumi; Azarakhsh Malekian; Rad Niazadeh |
| Abstract: | We consider descending price auctions for selling $m$ units of a good to unit demand i.i.d. buyers where there is an exogenous bound of $k$ on the number of price levels the auction clock can take. The auctioneer's problem is to choose price levels $p_1 > p_2 > \cdots > p_{k}$ for the auction clock such that auction expected revenue is maximized. The prices levels are announced prior to the auction. We reduce this problem to a new variant of prophet inequality, which we call \emph{batched prophet inequality}, where a decision-maker chooses $k$ (decreasing) thresholds and then sequentially collects rewards (up to $m$) that are above the thresholds with ties broken uniformly at random. For the special case of $m=1$ (i.e., selling a single item), we show that the resulting descending auction with $k$ price levels achieves $1- 1/e^k$ of the unrestricted (without the bound of $k$) optimal revenue. That means a descending auction with just 4 price levels can achieve more than 98\% of the optimal revenue. We then extend our results for $m>1$ and provide a closed-form bound on the competitive ratio of our auction as a function of the number of units $m$ and the number of price levels $k$. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.01384&r= |