EVALUATING DETERMINISTIC POLICIES IN TWO-PLAYER ITERATED GAMES

2009 ◽  
Vol 19 (12) ◽  
pp. 4039-4053
Author(s):  
RUI DILÃO ◽  
JOÃO GRACIANO
Keyword(s):  
Ergodic Theorem ◽  
Noncooperative Games ◽  
Equilibrium States ◽  
Statistical Ensemble ◽  
Equilibrium Solutions ◽  
Tit For Tat ◽  
The Mean ◽  
Finite Memory ◽  
Mean Payoff ◽  
Better Than

We construct a statistical ensemble of games, wherein each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the deterministic policies with finite memory. In particular, we show that if one of the players has a generalized tit-for-tat policy, the mean payoff per move of both players is the same, forcing the equalization of the mean payoffs per move. In the case of symmetric, noncooperative and dilemmatic games, we show that generalized tit-for-tat or imitation policies together with the condition of not being the first to defect, leads to the highest mean payoffs per move for the players. Within this approach, it can be decided which policies perform better than others. In particular, it shows that reciprocity in noncooperative iterated games forces equality of mean payoffs. We prove a simple ergodic theorem for symmetric and noncooperative games. The Prisoner's Dilemma and the Hawk–Dove games have been analyzed, and the equilibrium states of the infinitely iterated games have been determined. In infinitely iterated games with the player choosing their moves with equal probabilities, strict Nash solutions are not necessarily reachable equilibrium solutions of games.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

scholarly journals Decision and Coordination in a Dual-Channel Three-Layered Green Supply Chain

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 549 ◽  
Author(s):  
Zilong Song ◽  
Shiwei He ◽  
Baifeng An
Keyword(s):  
Sustainable Development ◽  
Supply Chain ◽  
Environmental Performance ◽  
Fresh Produce ◽  
Green Supply Chain ◽  
Market Demand ◽  
Equilibrium Solutions ◽  
Sustainable Performance ◽  
Dual Channel ◽  
Social And Environmental Performance

This paper investigated, for the first time, the game and coordination of a dual-channel, three-layered, green fresh produce supply chain, with regard to its economic, social, and environmental performance. Considering that the market demand is dual-channel priced and sensitive to the degree of greenness and the freshness-level, four game models, under different scenarios have been established. These included a centralized scenario, a decentralized scenario, and two contractual scenarios. The equilibrium solutions under the four scenarios were characterized. From the perspective of a sustainable development, the economic, social, and environmental performance of the supply chain was analyzed. To enhance the supply chain performance, two contract mechanisms were designed and the conditions for a multi-win outcome were obtained. Accordingly, many propositions and management implications were provided. The results showed that, (1) compared to the centralized supply chain case, the performance of the decentralized supply chain case is inferior; (2) in addition to increasing the concentration of the supply chain decisions, the two contracts proposed can effectively coordinate the green supply chain and improve its sustainable performance; and (3) the performance of the supply chain is positively driven by the consumers’ sensitivity to greenness degree and the freshness level of fresh produce. This paper fills a research gap and helps the participants of the channel recognize the operational decision principle of a complex green supply chain, in order to achieve a higher and a long-term sustainable-development performance.

scholarly journals Location-Specific Adjustments in Population and Employment across Metropolitan America

Urban Science ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 24
Author(s):  
Gordon F. Mulligan ◽  
John I. Carruthers
Keyword(s):  
Labor Markets ◽  
Metropolitan Areas ◽  
Adjustment Process ◽  
Equilibrium Solutions ◽  
Natural Amenities ◽  
Long Run ◽  
Local Sustainability ◽  
Universal Solution ◽  
Standard Linear ◽  
Local Solutions

This paper examines the joint adjustment of population and employment numbers across America’s metropolitan areas during the period 1990–2015. Current levels of both are estimated, for 10 year periods, using their lagged (own and cross) levels and eight other lagged variables. Population is affected by both human and natural amenities and employment by wages, patents, and other attributes of the workforce. This paper questions the conventional interpretation of the adjustment process by using geographically weighted regression (GWR) instead of standard linear (OLS, 2GLS) regression. Here the various estimates are all local, so the long-run equilibrium solutions for the adjustment process vary over space. Convergence no longer indicates a stable universal solution but instead involves a mix of stable and unstable local solutions. Local sustainability becomes an issue when making projections because employment can quickly lead or lag population in some metropolitan labor markets.

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

scholarly journals Decisions and Coordination in E-Commerce Supply Chain under Logistics Outsourcing and Altruistic Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 253
Author(s):  
Yuyan Wang ◽  
Zhaoqing Yu ◽  
Liang Shen ◽  
Runjie Fan ◽  
Rongyun Tang
Keyword(s):  
Supply Chain ◽  
Supply Chains ◽  
Stackelberg Game ◽  
Consumer Preferences ◽  
Third Party ◽  
Altruistic Behavior ◽  
Fixed Cost ◽  
Equilibrium Solutions ◽  
Factors Affecting ◽  
Dual Channel

Considering the peculiarities of logistics in the electronic commerce (e-commerce) supply chain (ESC) and e-commerce platform’s altruistic preferences, a model including an e-commerce platform, third-party logistics service provider, and manufacturer is constructed. Based on this, three decision models are proposed and equilibrium solutions are obtained by the Stackelberg game. Then, an “altruistic preference joint fixed-cost” contract is proposed to maximize system efficiency. Finally, numerical analysis is used to validate the findings of the paper. The article not only analyzes and compares the optimal decisions under different ESC models, but also explores the intrinsic factors affecting the decisions. This paper finds that the conclusions of dual-channel supply chains or traditional supply chains do not necessarily apply to ESC, and that the effect of altruistic behavior under ESC is influenced by consumer preferences. Moreover, there is a multiparty win–win state for ESC, and this state can be achieved through the “altruistic preference joint fixed-cost” contract. Therefore, the findings of this paper contribute to the development of an e-commerce market and the cooperation of ESC members.

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