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on Game Theory |
| By: | Herold, Florian; Kuzmics, Christoph |
| Abstract: | In a finite two player game consider the matrix of one player's payoff difference between any two consecutive pure strategies. Define the half space induced by a column vector of this matrix as the set of vectors that form an obtuse angle with this column vector. We use Farkas' lemma to show that this player can be made indifferent between all pure strategies if and only if the union of all these half spaces covers the whole vector space. This result leads to a necessary (and almost sufficient) condition for a game to have a completely mixed Nash equilibrium. We demonstrate its usefulness by providing the class of all symmetric two player three strategy games that have a unique and completely mixed symmetric Nash equilibrium. |
| Keywords: | completely mixed strategies, mixed Nash equilibria, Farkas’, lemma |
| JEL: | C72 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bamber:289614&r=gth |
| By: | Bora Yongacoglu; G\"urdal Arslan; Lacra Pavel; Serdar Y\"uksel |
| Abstract: | Weakly acyclic games generalize potential games and are fundamental to the study of game theoretic control. In this paper, we present a generalization of weakly acyclic games, and we observe its importance in multi-agent learning when agents employ experimental strategy updates in periods where they fail to best respond. While weak acyclicity is defined in terms of path connectivity properties of a game's better response graph, our generalization is defined using a generalized better response graph. We provide sufficient conditions for this notion of generalized weak acyclicity in both two-player games and $n$-player games. To demonstrate that our generalization is not trivial, we provide examples of games admitting a pure Nash equilibrium that are not generalized weakly acyclic. The generalization presented in this work is closely related to the recent theory of satisficing paths, and the counterexamples presented here constitute the first negative results in that theory. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.18086&r=gth |
| By: | Calvia, Alessandro (Center for Mathematical Economics, Bielefeld University); Federico, Salvatore (Center for Mathematical Economics, Bielefeld University); Ferrari, Giorgio (Center for Mathematical Economics, Bielefeld University); Gozzi, Fausto (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study. |
| Keywords: | mean-field games, mean-field equilibrium, forward-backward ODEs, optimal investment, price formation |
| Date: | 2024–04–09 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:690&r=gth |
| By: | Ashkenazi-Golan, Galit; Tsodikovich, Yevgeny; Viossat, Yannick |
| Abstract: | A common practice in many auctions is to offer bidders an opportunity to improve their bids, known as a best and final offer stage. This improved bid can depend on new information either about the asset or about the competitors. This paper examines the effects of new information regarding competitors, seeking to determine what information the auctioneer should provide assuming the set of allowable bids is discrete. The rational strategy profile that maximizes the revenue of the auctioneer is the one where each bidder makes the highest possible bid that is lower than his valuation of the item. This strategy profile is an equilibrium for a large enough number of bidders, regardless of the information released. We compare the number of bidders needed for this profile to be an equilibrium under different information structures. We find that it becomes an equilibrium with fewer bidders when less additional information is made available to the bidders regarding the competition. It follows that when the number of bidders is a priori unknown, there are some advantages to the auctioneer not revealing information and conducting a one-stage auction instead. |
| Keywords: | auctions; BAFO; information utilization; multistage auctions; NSFC-ISF; China Grant #2510/17. Y |
| JEL: | D44 D82 |
| Date: | 2023–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:118706&r=gth |
| By: | Daniel Krähmer |
| Abstract: | The paper studies the canonical hold-up problem with one-sided investment by the buyer and full ex post bargaining power by the seller. The buyer can covertly choose any distribution of valuations at a cost and privately observes her valuation. The main result shows that in contrast to the well-understood case with linear costs, if investment costs are strictly convex in the buyer’s valuation distribution, the buyer’s equilibrium utility is strictly positive and to- tal welfare is strictly higher than in the benchmark when valuations are public information, thus alleviating the hold-up problem. In fact, when costs are mean-based or display decreas- ing risk, the hold-up problem may disappear completely. Moreover, the buyer’s equilibrium utility and total welfare might be non-monotone in costs. The paper utilizes an equilibrium characterization in terms of the Gateaux derivative of the cost function. |
| Keywords: | Information Design, Hold-Up Problem, Unobservable Information |
| JEL: | C61 D42 D82 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_523&r=gth |
| By: | William Brock; Anastasios Xepapadeas |
| Abstract: | Scientific evidence suggests that anthropogenic impacts on the environment, such as land-use changes and climate change, promote the emergence of infectious diseases (IDs) in humans. We provide a synthesis which captures interactions between the economy and the natural world and links climate, land-use and IDs. We develop a two-region integrated epidemic-economic model which unifies short-run disease containment policies with long-run policies which could control the drivers and the severity of IDs. We structure our paper by linking susceptible-infected-susceptible and susceptible-infected-recovered models with an economic model which includes land-use choices for agriculture, climate change and accumulation of knowledge that supports land-augmenting technical change. The ID contact number depends on short-run policies (e.g., lockdowns, vaccination), and long-run policies affecting land-use, the natural world and climate change. Climate change and land-use change have an additional cost in terms of IDs since they might increase the contact number in the long-run. We derive optimal short-run containment controls for a Nash equilibrium between regions, and long-run controls for climate policy, land-use, and knowledge at an open loop Nash equilibrium and the social optimum and unify the short- and long-run controls. We explore the impact of ambiguity aversion and model misspecification in the unified model and provide simulations which support the theoretical model. |
| Keywords: | infectious diseases, SIS and SIR models, natural world, climate change, land-use, containment, Nash equilibrium, OLNE, social optimum, land-augmenting technical change |
| JEL: | I18 Q54 D81 |
| Date: | 2024–03–29 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:2409&r=gth |
| By: | Cardullo, Gabriele (University of Genova) |
| Abstract: | Although European institutions and national governments have long pushed for a more decentralized wage bargaining structure, in some countries company or establishment-level negotiations struggle to take place. This paper offers an interpretation for that based on workers' optimal choices in an strategic framework. I construct an equilibrium matching model that explains under which conditions it is best for workers to negotiate their entire wage at sectoral level (one-tier bargaining) or to let a fraction of their salary to be negotiated at company level (two-tier bargaining). Workers' strategies do not simply depend on their own characteristics or on those of their firm, but also on the decisions of all the other employees of the sector. Three alternative Nash equilibria may occur: one-tier bargaining for all workers; two-tier bargaining for all workers; two-tier bargaining for the most productive workers and one-tier bargaining for the others. The prevalence of a specific equilibrium over others hinges on some critical factors, notably the elasticity of the matching function and the properties of the productivity distribution. |
| Keywords: | bargaining structure, wage decentralization, collective bargaining, unions |
| JEL: | J50 J52 J31 J64 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp16870&r=gth |
| By: | KATO, Hiroki; KIM, Youngrok |
| Abstract: | Donors entrust their resources to charitable organizations, which use these to carry out activities that contribute to society. Thus, the donation market carries the potential for moral hazard on the part of charitable organizations. However, empirical insights into the negative consequences of this problem are scarce. This study creates a unique game by incorporating elements of principal-agent relationships into the dictator game, in order to quantitatively examine the consequences of moral hazard in the donation market through laboratory experiments. The results reveal that moral-hazard environments hinder the average donation amount from donors and, furthermore, decrease recipients’ average payoffs. To address this negative outcome, non-binding promises are introduced to inform donors beforehand of the actions to be taken by charitable organizations. Although these promises succeed in offsetting the decrease in donation amounts, they do not sufficiently improve recipient welfare. |
| Keywords: | Charity market, Dictator game, Fraud, Hidden action, Promise |
| JEL: | C71 C92 D64 D82 |
| Date: | 2024–04–02 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hiasdp:hias-e-139&r=gth |
| By: | José Mª Durán-Cabré (Universitat de Barcelona & IEB); Alejandro Esteller-Moré (Universitat de Barcelona & IEB); Daniel Montolio (Universitat de Barcelona & IEB); Javier Vázquez-Grenno (Universitat de Barcelona & IEB) |
| Abstract: | In a two-country model, the citizens of a ‘big home country’ can either fictitiously move residence to a ‘small foreign country’ where residence-based taxes are lower (external tax avoidance), or under-report the tax base at home (internal tax avoidance). Tax setting is the result of Cournot-Nash competition between revenue maximizing governments, with the home government also setting two types of administration policies, one for each form of tax avoidance. We show that although it is optimal to employ both types of administration policies, which in themselves are both effective at tackling the targeted form of tax avoidance, the optimum is characterized by a tradeoff in terms of policy outcomes: either internal avoidance increases and external avoidance decreases, or the opposite, depending on the characteristics of the fiscal environment. |
| Keywords: | Tax perceptions/preferences, experimental design, student/teacher gender bias |
| JEL: | A23 H20 I2 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ieb:wpaper:doc2024-02&r=gth |
| By: | Shigehiro Serizawa; Natsumi Shimada; Tiffany Tsz Kwan Tse |
| Abstract: | This study explores two key factors influencing subjects’ deviation from dominant bidding in Vickrey auction experiments. The first factor examines subjects’ understanding of strategy-proofness (SP), while the second focuses on “human interaction” which includes social preferences (spite and altruism), responses to strategic uncertainty, and tacit collusion. To analyze the effect of understanding SP, we quiz subjects before an experimental Vickrey auction and examine whether their bidding behavior changes if one of the quizzes includes hints about SP. We design the quiz carefully, incorporating implicit hints about SP and ensuring the avoidance of explicit demands or advice to mitigate experimenter demand effects. However, completing the quiz enables the subjects to understand SP themselves. To analyze the effects of human interaction, we examine whether subjects’ bidding behavior changes if they compete against robots instead of human rivals in the auctions. We design 2 × 2 treatments by varying the type of quiz (with or without hints about SP) and the nature of the rivals (humans or robots). We found that the quiz with hints about SP increases dominant bidding. The nature of rivals also influences the bidding behavior; nonetheless, its impact is not as robust as that of SP hints. Thus, the main factor causing dominated bidding in Vickrey auction experiments is not human interaction but a lack of understanding of SP. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1229r&r=gth |
| By: | Timothy Hunt |
| Abstract: | I analyse strategic interaction between adult siblings in the provision of care to an elderly parent by estimating a dynamic discrete-choice game in which siblings make location, work and care choices. I find that the opportunity for strategic play exacerbates gender differences in caring responsibilities as sons in particular strategically shirk providing care as they believe their sibling is relatively likely to provide care in their absence. Counterfactual experiments show that if siblings instead took care, location and work choices independently then the gender care gap would be around 14% smaller. Also, I find that unobserved preference differences between sons and daughters are far more important in driving the gender care gap than observed differences in wages. |
| Date: | 2024–02–29 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:1042&r=gth |
| By: | Zhuo Chen; Yun Liu |
| Abstract: | This paper proposes a dynamic research contest, namely the chasing contest, in which two asymmetric contestants exert costly effort to accomplish two breakthroughs in a continuous-time framework. The contestants are asymmetric in that one of them is present-biased and has already achieved one breakthrough (the leader), while the other is time-consistent and needs to achieve two breakthroughs to win (the chaser). The principal can choose between two disclosure policies, which either immediately announces the first breakthrough of the chaser (public chasing contest), or only announces the contest results until its terminus (hidden chasing contest). We fully characterize the unique x-start and y-stop equilibrium of the chasing contest with the two disclosure policies, in which the leader starts working from an instant x to the end while the chaser stops exerting effort by the instant y. We further compare the asymmetric incentives of the two disclosure policies. Our results imply that the chaser will never stop earlier in the hidden chasing contest compared to its public chasing counterpart, whereas the leader works longer in the public chasing contest only if the contest permits a late deadline. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.02756&r=gth |
| By: | Simon Cowan |
| Abstract: | General conditions that are sufficient for mergers in symmetric Cournot industries to be profitable or unprofitable are found and applied. If inverse demand curvature is weakly higher than the number of firms then all mergers are profitable. The same condition implies that outputs are strategic complements locally. If demand is log-concave, so inverse demand curvature is at most 1, two-firm mergers are unprofitable. Log-concavity of demand implies that outputs are strategic substitutes. The issue of the profitability of mergers in Cournot was first addressed by Salant, Switzer, and Reynolds (1983) in a model with linear demand. |
| Date: | 2024–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:1041&r=gth |
| By: | Gächter, Simon (University of Nottingham); Kaiser, Esther (Zurich University of Applied Sciences (ZHAW)); Königstein, Manfred (University of Erfurt) |
| Abstract: | Explicit and implicit incentives and opportunities for mutually beneficial voluntary cooperation co-exist in many contractual relationships. In a series of eight laboratory gift-exchange experiments, we show that incentive contracts can lead to crowding out of voluntary cooperation even after incentives have been abolished. This crowding out occurs also in repeated relationships, which otherwise strongly increase effort compared to one-shot interactions. Using a unified econometric framework, we unpack these results as a function of positive and negative reciprocity, as well as the principals' wage offer and the incentive-compatibility of the contract. Crowding out is mostly due to reduced wages and not a change in reciprocal wage-effort relationships. Our systematic analysis also replicates established results on gift exchange, incentives, and crowding out of voluntary cooperation while exposed to incentives. Overall, our findings show that the behavioral consequences of explicit incentives strongly depend on the features of the situation in which they are embedded. |
| Keywords: | principal-agent games, gift-exchange experiments, incomplete contracts, explicit incentives, implicit incentives, repeated games, crowding out |
| JEL: | C70 C90 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp16872&r=gth |
| By: | Ezzat Elokda; Heinrich Nax; Saverio Bolognani; Florian D\"orfler |
| Abstract: | A system of non-tradable credits that flow between individuals like karma, hence proposed under that name, is a mechanism for repeated resource allocation that comes with attractive efficiency and fairness properties, in theory. In this study, we test karma in an online experiment in which human subjects repeatedly compete for a resource with time-varying and stochastic individual preferences or urgency to acquire the resource. We confirm that karma has significant and sustained welfare benefits even in a population with no prior training. We identify mechanism usage in contexts with sporadic high urgency, more so than with frequent moderate urgency, and implemented as an easy (binary) karma bidding scheme as particularly effective for welfare improvements: relatively larger aggregate efficiency gains are realized that are (almost) Pareto superior. These findings provide guidance for further testing and for future implementation plans of such mechanisms in the real world. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.02687&r=gth |
| By: | Marco de Pinto (University of Applied Labour Studies); Laszlo Goerke (Institute for Labour Law and Industrial Relations in the European Union (IAAEU), Trier University); Alberto Palermo (University of Roehampton) |
| Abstract: | Entry in a homogeneous Cournot oligopoly can be excessive if there is business stealing. Since this excessive entry prediction has been established, a variety of circumstances have been identified which allow for insufficient entry, despite the business stealing externality. This paper shows that most of them rely on the same mechanism and, therefore, constitute a special case of a general set-up. To establish this insight, we survey the pertinent contributions and classify the circumstances, which are invoked to establish the possibility of insufficient entry into four categories. Importantly, they all imply that the oligopolists pay a rent, which reduces profits and deters entry. Since rents are welfare-neutral, insufficient entry will occur if the rent is high enough. |
| Keywords: | : Business stealing, Cournot oligopoly, Economic rent, Excessive entry, Insufficient entry, Literature survey |
| JEL: | D43 D62 L13 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:iaa:dpaper:202402&r=gth |
| By: | Touhami Abdelkhalek; Dorothee Boccanfuso |
| Abstract: | Public policies, particularly those related to taxes and subsidies, should help to reduce poverty and inequality. However, the combination of components of these two systems, as implemented, leads sometimes to an increase in poverty and or inequality without being necessarily anticipated. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:ocp:ppaper:pb42-23&r=gth |
| By: | Hoang Hiep Nguyen (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Jean-Laurent Viviani (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Sami Ben Jabeur (ESDES - ESDES, Lyon Business School - UCLy - UCLy - UCLy (Lyon Catholic University), UCLy - UCLy (Lyon Catholic University)) |
| Abstract: | Recently, ensemble-based machine learning models have been widely used and have demonstrated their efficiency in bankruptcy prediction. However, these algorithms are black box models and people cannot understand why they make their forecasts. This explains why interpretability methods in machine learning attract attention from many artificial intelligence researchers. In this paper, we evaluate the prediction performance of Random Forest, LightGBM, XGBoost, and NGBoost (Natural Gradient Boosting for probabilistic prediction) for French firms from different industries with the horizon of 1-5 years. We then use Shapley Additive Explanations (SHAP), a model-agnostic method to explain XGBoost, one of the best models for our data. SHAP can show how each feature impacts the output from XGBoost. Furthermore, single prediction can also be explained, thus allowing black box models to be used in credit risk management. |
| Keywords: | Shapley additive explanations, Explainable machine learning, Bankruptcy prediction, Ensemble-based model, XGBoost |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04223161&r=gth |