A Large Population Partnership Formation Game with Associative Preferences and Continuous Time

• Autorzy: Ramsey D. M.

Identyfikatory

DOI

10.14708/ma.v46i2.5128

Warianty tytułu

PL

Gra o typie wyboru partnera z kontinuum graczy, preferencjami homotypowymi oraz czasem ciągłym

• Języki publikacji: EN

Abstrakty

EN

A model of partnership formation is considered in which there are two classes of player (called male and female). There is a continuum of players and two types of both sexes. These two types can be interpreted, e.g. as two subspecies, and each searcher prefers to pair with an individual of the same type. Players Begin searching at time zero and search until they find a mutually acceptable prospective partner or the mating season ends. When a pair is formed, both individuals leave the pool of searchers. Hence, the proportion of players still searching and the distribution of types changes over time. Prospective partners are found at a rate which is nondecreasing in the proportion of players still searching. Nash equilibria are derived which satisfy a refinement based on the following optimality criterion: each searcher accepts a prospective partner if and only if the reward that would be gained from such a partnership (given that it formed) is greater or equal to the expected reward obtained by that searcher from future search. So called "completely symmetric" versions of this game are considered, where the two types of player are equally frequent. In this class of games, there exists a unique Nash equilibrium satisfying the optimality criterion, regardless of the precise rule determining the rate at chich prospective partners are found. This equilibrium is given by a threshold time t₀, such that before time t₀ individuals only mate with prospective partners of the same type and from time t₀ onwards each searcher accepts any prospective partner. Two examples are given. One example considers the so called "singles bar" model, according to which prospective partners are found at a constant rate. The secondo example considers the "mixing population" model, according to which the rate at which prospective partners are found is proportional to the fraction of individuals who are still searching for a partner.

PL

Rozważane będą modele matematyczne, w których zmiana parametru jest przedmiotem badań statystycznych. Specjalizowanym narzędziem do tego celu są karty kontrolne. Celem pracy jest konstrukcja kart kontrolnych do badania zmian parametru rozkładu obserwowanej cechy w oparciu o dokładne rozkłady różnych estymatorów parametrów kontrolowanych wielkości i ich porównanie.

Słowa kluczowe

EN

partnership formation; dynamic game; Nash equilibrium; stopping problem

PL

tworzenie partnerstwa; gra dynamiczna; równowaga Nasha; problem stopowania

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2018
• Tom: Vol. 46, no. 2
• Strony: 171--195
• Opis fizyczny: Bibliogr. 31 poz., fot., tab., wykr.

Twórcy

autor

Ramsey D. M.

• Wrocław University of Science and Technology, Faculty of Computer Science and Management, Wybrzeże Wyspiańskiego 27, Wrocław 50-370, Poland

Bibliografia

• [1] H. Adachi. A search model of two-sided matching under nontransferable utility. J. Econom. Theory, 113 (2): 182-198, 2003. ISSN 0022-0531. doi: 10.1016/S0022-0531(03)00085-1. URL https://doi.org/10.1016/S0022-0531(03)00085-1. Cited on p. 173.
• [2] S. Alpern and I. Katrantzi. Equilibria of two-sided matching games with common preferences. European J. Oper. Res., 196 (3): 1214-1222, 2009. ISSN 0377-2217. doi: 10.1016/j.ejor.2008.05.012. URL https://doi.org/10.1016/j.ejor.2008.05.012. Cited on p. 173.
• [3] S. Alpern and D. Reyniers. Strategic mating with homotypic preferences. Journal of Theoretical Biology, 198 (1): 71-88, 1999. ISSN 0022-5193. doi: 10.1006/jtbi.1999.0903. Cited on p. 172.
• [4] S. Alpern and D. Reyniers. Strategic mating with common preferences. J. Theoret. Biol., 237 (4): 337-354, 2005. ISSN 0022-5193. doi: 10.1016/j.jtbi.2003.09.021. Cited on p. 173.
• [5] C. T. Bergstrom and L. A. Real. Towards a theory of mutual mate choice: Lessons from two-sided matching. Evol. Ecol. Res., 2: 493-508, 2000. URL http://www.evolutionary-ecology.com/abstracts/v02/1212.html. Cited on p. 173.
• [6] A. C. Janetos. Strategies of female mate choice: A theoretical analysis. Behavioral Ecology and Sociobiology, 7 (2): 107-112, 1980. ISSN 03405443, 14320762. doi: 10.2307/4599314. Cited on p. 172.
• [7] B. Kenneth and C. M. G. Long-term partnership formation: Marriage and employment. The Economic Journal, 109 (456): 307-334, 1999. doi: 10.1111/1468-0297.00435. URL https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0297.00435. Cited on p. 173.
• [8] L. Real. Search theory and mate choice. i. models of single-sex discrimination. The American Naturalist, 136 (3): 376-405, 1990. doi: 10.1086/285103. Cited on p. 172.
• [9] G. J. Stigler. The economics of information. Journal of Political Economy, 69 (3): 213-225, 1961. doi: 10.1086/258464. Cited on p. 171.
• [10] Castellano, S., Cadeddu, G., and Cermelli, P. (2012). Computational mate choice: theory and empirical evidence. Behavioural Processes, 90 (2), 261-277. Cited on p. 191.
• [11] Chiappori P. A. and Salanié B. (2016). The econometrics of matching models. Journal of Economic Literature, 54 (3), 832-861. Cited on p. 173.
• [12] Chow, Y. S. (1971). Great expectations. The theory of optimal stopping. Houghton Mifflin, Boston, MA Cited on pp. 178 and 182.
• [13] Collins E. J. and McNamara J. M. (1993). The job-search problem with competition: an evolutionarily stable strategy. Advances in Applied Probability, 25, 314-333. Cited on p. 173.
• [14] Courtiol, A., Etienne, L., Feron, R., Godelle, B., and Rousset, F. (2016).The evolution of mutual mate choice under direct benefits. The American Naturalist, 188 (5), 521-538. Cited on p. 174.
• [15] Dechaume-Moncharmont, F. X., Brom, T., and Cézilly, F. (2016). Opportunity costs resulting from scramble competition within the choosy sex severely impair mate choosiness. Animal Behaviour, 114, 249-260. Cited on pp. 173 and 178.
• [16] Etienne, L., Rousset, F., Godelle, B. and Courtiol, A. (2014). How chaosy should I be? The relative searching time predicts evolution of choosiness under direct sexual selection. Proceedings of the Royal Society B, 281, 20140190. Cited on p. 174.
• [17] Gale, D. and Shapley, L. S. (1962). College admissions and the stability of marriage. The American Mathematical Monthly, 69 (1), 9-15. Cited on p. 172.
• [18] Johnstone R. A. (1997). The tactics of mutual mate choice and competitive search. Behavioural and Ecological Sociobiology, 40, 51-59. Cited on p. 173.
• [19] Lauermann S. and Nöldeke G. (2014). Stable marriages and search friction. Journal of Economic Theory, 151, 163-195. Cited on p. 173.
• [20] Mazalov V. and Falko A. (2008). Nash equilibrium in two-sided mate choice problem. International Game Theory Review, 10 (4), 421-435. Cited on p. 173.
• [21] McNamara J. M. and Collins E. J. (1990). The job search problem as an employer-candidate game. Journal of Applied Probability, 28, 815-827. Cited on pp. 172, 178, and 189.
• [22] McNamara J. M., Szekely T., Webb J. N. and Houston A. I. (2000). A dynamic game-theoretic model of parental care. Journal of Theoretical Biology, 205 (4), 605-623. Cited on p. 175.
• [23] Parker G. A. (1983). Mate quality and mating decisions. In: Mate Choice (Bateson P. ed.), pp. 227-256. Cambridge University Press, Cambridge. Cited on p. 172.
• [24] Priklopil, T., Kisdi, E., and Gyllenberg, M. (2015). Evolutionarily stable mating decisions for sequentially searching females and the stability of reproductive isolation by assortative mating. Evolution, 69 (4), 1015-1026. Cited on p. 174.
• [25] Ramsey D. M. (2008). A large population job search game with discrete time. European Journal of Operational Research, 188, 586-602. Cited on pp. 173 and 191.
• [26] Ramsey D. M. (2008). On a large population partnership formation game with continuous time. Contributions to Game Theory and Management, 8, 268-277. Cited on p. 174.
• [27] Ramsey, D. M. (2012). Partnership formation based on multiple traits. European Journal of Operational Research, 216 (3), 624-637. Cited on p. 172.
• [28] Real L. A. (1991). Search theory and mate choice. II. Mutual interaction, assortative mating, and equilibrium variation in male and female fitness. American Naturalist, 138, 901-917. Cited on p. 172.
• [29] Shimer R. and Smith L. (2000). Assortative matching and search. Econometrica, 68, 343-369. Cited on p. 173.
• [30] Smith L. (2006). The marriage model with search frictions. Journal of Political Economy, 114, 1124-1144. Cited on p. 173.
• [31] Wu Q. (2015). A finite decentralized marriage market with bilateral search. Journal of Economic Theory, 160, 216-242. Cited on p. 173.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).