|
on Game Theory |
| By: | Peter A. Streufert (University of Western Ontario) |
| Abstract: | This paper uses value functions to characterize the pure-strategy subgame-perfect equilibria of an arbitrary, possibly infinite-horizon game. It specifies the game’s extensive form as a pentaform (Streufert 2023p, arXiv:2107.10801v4), which is a set of quintuples formalizing the abstract relationships between nodes, actions, players, and situations (situations generalize information sets). Because a pentaform is a set, this paper can explicitly partition the game form into piece forms, each of which starts at a (Selten) subroot and contains all subsequent nodes except those that follow a subsequent subroot. Then the set of subroots becomes the domain of a value function, and the piece-form partition becomes the framework for a value recursion which generalizes the Bellman equation from dynamic programming. The main results connect the value recursion with the subgame-perfect equilibria of the original game, under the assumptions of upper- and lower-convergence. Finally, a corollary characterizes subgame perfection as the absence of an improving one-piece deviation. |
| Keywords: | Bellman equation, value function, upper-convergence, lower-convergence, pentaform |
| JEL: | C61 C73 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:uwo:uwowop:20233&r=gth |
| By: | ShinichiIshihara (Waseda Institute of Political Economy Waseda University); Junnosuke Shino (School of International Liberal Studies, Waseda University) |
| Abstract: | Interval games are an extension of cooperative coalitional games in which players are assumed to face payoff uncertainty as represented by a closed interval. In this study, we examine two interval game versions of Shapley values (i.e., the interval Shapley value and the interval Shapley like value), and characterize them using an axiomatic approach. For the interval Shapley value, we show that the existing axiomatization can be generalized to a wider subclass of interval games called size monotonic games. For the interval Shapley-like value, we show that a standard axiomatization using Young’s strong monotonicity holds on the whole class of interval games. |
| Keywords: | cooperative interval games; interval uncertainty; Shapley value; axiomatization |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:2214&r=gth |
| By: | Rafat Beigpoor Shahrivar; Duesterhoeft, Ilka; Rogna, Marco; Vogt, Carla |
| Abstract: | Public good games in coalitional form, such as the ones depicting international environmental agreements for the reduction of a global pollutant, generally foresee scarce levels of cooperation. The incentive to free ride, that increases for higher levels of cooperation, prevents the formation of stable coalitions. The introduction of other-regarding preferences, in the form of Fehr and Schmidt utility functions, enlarges cooperation, but still at suboptimal levels. The present paper considers a further possibility, namely the introduction of a mechanism through which the contributions of players to the public good are proportional to the average contribution of the other players abiding to the mechanism: proportional contributions. The mechanism is therefore rooted into reciprocity. By applying it to a standard abatement game parameterized on the RICE model, we show that the mechanism is in fact able to increase cooperation both under standard and under F&S preferences. Stability of the grand coalition is never reached, but potential internally stable grand coalitions are achieved under F&S preferences. The attainment of higher cooperation comes at the expense of the level of global abatement that is lower when proportional contributions are in place. |
| Keywords: | Coalitional game, cooperation, F&S preferences, public good, reciprocity |
| JEL: | C72 D63 H41 Q54 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:990&r=gth |
| By: | Ohta, Katsunori; Tamura, Yuji |
| Abstract: | Resettlement is one means of assisting refugees to regain self-reliant living with- out constant fear. The global total of resettled refugees has remained fractional relative to the need. To contribute to the ongoing effort to increase resettlement, we consider self-enforceable sharing of full resettlement through analysis of a repeated game at the beginning of which host countries bargain over their shares. We find that cooperation opportunities are diminished, or else lost, by cutting the cost of resettlement, whereas they are expanded by heightened pureness in treating refugee protection as a humanitarian public good. Our finding thus makes us reconsider the implications of static-game analysis that both high cost and public-good nature of refugee protection are the sources of insuffi cient admission. We also show that a wide range of cooperation opportunities may not be conducive to the effi ciency of an equilibrium outcome because it allows the bargaining outcome to deviate from the effi cient one. We suggest policies for creating cooperation opportunities and improving equilibrium effi ciency. Our framework is suffi ciently general and is useful for examining other similar problems of public-good provision. |
| Keywords: | International cooperation, International public good, Noncooperative game, Repeated game, Alternate-offer bargaining |
| JEL: | H41 H87 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:1237&r=gth |
| By: | Vijay V. Vazirani |
| Abstract: | The core is a dominant solution concept in economics and game theory. In this context, the following question arises, ``How versatile is this solution concept?'' We note that within game theory, this notion has been used for profit -- equivalently, cost or utility -- sharing only. In this paper, we show a completely different use for it: in an {\em investment management game}, under which an agent needs to allocate her money among investment firms in such a way that {\em in each of exponentially many future scenarios}, sufficient money is available in the ``right'' firms so she can buy an ``optimal investment'' for that scenario. We study a restriction of this game to {\em perfect graphs} and characterize its core. Our characterization is analogous to Shapley and Shubik's characterization of the core of the assignment game. The difference is the following: whereas their characterization follows from {\em total unimodularity}, ours follows from {\em total dual integrality}. The latter is another novelty of our work. |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2302.00608&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Xavier Venel (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma], PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two characteristics: the network structure and the diffusion mechanism represented by an aggregation function. We distinguish between two diffusion mechanisms (probabilistic, deterministic) and focus on two types of aggregation functions (strict, Boolean). Under strict aggregation functions, polarization of the society cannot happen, and its state evolves towards a mixture of infinitely many active and infinitely many inactive agents, or towards a homogeneous society. Under Boolean aggregation functions, the diffusion process becomes deterministic and the contagion model of Morris (2000) becomes a particular case of our framework. Polarization can then happen. Our dynamics also allows for cycles in both cases. The network structure is not relevant for these questions, but is important for establishing irreducibility, at the price of a richness assumption: the network should contain at least one complex star and have enough space for storing local configurations. Our model can be given a game-theoretic interpretation via a local coordination game, where each player would apply a best-response strategy in a random neighborhood. |
| Keywords: | diffusion, countable network, aggregation function, polarization, convergence, bestresponse |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:pseptp:halshs-03881455&r=gth |
| By: | Behnaz Minooei Fard; Willi Semmler; Giovanni Di Bartolomeo |
| Abstract: | The economics of rare earth elements (REEs) has become a critical issue due to the growing demand for these crucial materials in the transition to renewable energies. The monopolistic structure of the REE market dominated by China and its unstable supply of REEs has raised concerns globally about potential supply chain disruptions. With the largest REE reserves and refining capacity, China exerts market power, causing supply chain problems and price volatility. However, China's growing consumption of REEs may exceed its domestic production and lose its control over the supply since other countries move into the market. This paper uses a game-theoretic stylization to examine competition between China and the rest of the world (ROW). We investigate how China uses a limit-pricing mechanism to prevent the entrance of fringe firms from the ROW and show how the ROW is limited to quantity adjustments. We also examine the market's transformation from a monopoly to a foreseeable duopoly. The focus is on the supply side of the market, the resource extraction by China and the ROW, and the depletion of the discovered resources. Additionally, we assess the role of the impact of marginal costs and supporting policies on these dynamics. Our model variants are solved numerically using the moving-horizon strategy in differential games provided by the non-linear model predictive control (NMPC) technique, allowing us to predict the outcome of the interaction between China and the ROW and the impact of their decision-making. |
| Keywords: | Rare earth elements; differential games; non-linear model predictive control |
| JEL: | C61 C7 Q3 |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:sap:wpaper:wp235&r=gth |
| By: | Thomas Dohmen (University of Bonn, IZA Institute of Labor Economics, Maastricht University); Simone Quercia (University of Verona); Jana Willrodt (Düsseldorf Institute for Competition Economics (DICE)) |
| Abstract: | In this paper, we hypothesize that the strength of the consensus effect, i.e., the tendency for people to overweight the prevalence of their own values and preferences when forming beliefs about others’ values and preferences, depends on the salience of own preferences. We manipulate salience by varying the order of elicitation of preferences and beliefs. Although our results confirmthe existence of the consensus effect, we find no evidence of a difference between the two orders of elicitation. While our results highlight the robustness of the consensus effect, they also indicate that salience does not mediate the strength of this phenomenon. |
| Keywords: | Consensus effect, social preferences, trust game, beliefs |
| JEL: | C91 D01 D83 D91 |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:219&r=gth |