Game theory
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... Contents -- Preface -- 1 Decision-Theoretic Foundations -- 1.1 Game Theory, Rationality, and Intelligence ... ... Repeated Games 310 -- 7.3 Stationary Equilibria of Repeated Games with Complete State Information and ... ... Theorems for Standard Repeated Games 331 -- 7.6 Finitely Repeated Games and the Role of Initial Doubt ... ... Simulation of Repeated Games 364 Exercises 365 -- 8 Bargaining and Cooperation in Two-Person Games 370 ... ... -- 8.1 Noncooperative Foundations of Cooperative Game Theory 370 -- 8.2 Two-Person Bargaining Problems ...
1st Harvard University Press paperback ed. xiii, 568 s. : il. ; 24 cm
- MeSH
- matematika MeSH
- teorie her MeSH
- Publikační typ
- monografie MeSH
- Konspekt
- Matematika
- NLK Obory
- přírodní vědy
In practical use we know and quite widely use mathematical methods that lead to process of optimization. In a special group of such methods we recognize schemes, which are used in those cases when different opponents with antagonistic interests compete with one another. On the example of shooting in ice hockey we have demonstrated a use of theory of games. The antagonistic situation exists between shooter (which has two main possibilities - to shoot right above the ice or to the upper part of the goal) and goalkeeper (not to set off or set off against the shot puck and stand or kneel). We have created special pay-off matrices with „cost“ of different strategic possibilities to be able to find the optimal strategic - in our sample - matrix saddle point. These optimal strategies are following - main activity of goalkeeper is setting off against shot pucks and kneeling, on the other hand the shooter should shoot the puck to upper part of the goal. The example also showed the part of the mathematical model that seems to be extraordinary useful at sports.
We develop a decision tree based game-theoretical approach for constructing functional responses in multi-prey/multi-patch environments and for finding the corresponding optimal foraging strategies. Decision trees provide a way to describe details of predator foraging behavior, based on the predator's sequence of choices at different decision points, that facilitates writing down the corresponding functional response. It is shown that the optimal foraging behavior that maximizes predator energy intake per unit time is a Nash equilibrium of the underlying optimal foraging game. We apply these game-theoretical methods to three scenarios: the classical diet choice model with two types of prey and sequential prey encounters, the diet choice model with simultaneous prey encounters, and a model in which the predator requires a positive recognition time to identify the type of prey encountered. For both diet choice models, it is shown that every Nash equilibrium yields optimal foraging behavior. Although suboptimal Nash equilibrium outcomes may exist when prey recognition time is included, only optimal foraging behavior is stable under evolutionary learning processes.
- MeSH
- predátorské chování MeSH
- teoretické modely * MeSH
- teorie her * MeSH
- zvířata MeSH
- Check Tag
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Pomocí teorie her se autor zamýšlí nad motivací posudkového lékaře při výkonu jeho činnosti s tím, do jaké míry je motivován posuzovanému nevyhovět v jeho požadavcích.
Using the play theory, the author reflects on motivation of a physician reviewer not to respond to requirements of the assessed person.
Classic bimatrix games, that are based on pair-wise interactions between two opponents in two different roles, do not consider the effect that interaction duration has on payoffs. However, interactions between different strategies often take different amounts of time. In this article, we further develop a new approach to an old idea that opportunity costs lost while engaged in an interaction affect individual fitness. We consider two scenarios: (i) individuals pair instantaneously so that there are no searchers, and (ii) searching for a partner takes positive time and populations consist of a mixture of singles and pairs. We describe pair dynamics and calculate fitnesses of each strategy for a two-strategy bimatrix game that includes interaction times. Assuming that distribution of pairs (and singles) evolves on a faster time scale than evolutionary dynamics described by the replicator equation, we analyze the Nash equilibria (NE) of the time-constrained game. This general approach is then applied to the Owner-Intruder bimatrix game where the two strategies are Hawk and Dove in both roles. While the classic Owner-Intruder game has at most one interior NE and it is unstable with respect to replicator dynamics, differences in pair duration change this prediction in that up to four interior NE may exist with their stability depending on whether pairing is instantaneous or not. The classic game has either one (all Hawk) or two ((Hawk,Dove) and (Dove,Hawk)) stable boundary NE. When interaction times are included, other combinations of stable boundary NE are possible. For example, (Dove,Dove), (Dove,Hawk), or (Hawk,Dove) can be the unique (stable) NE if interaction time between two Doves is short compared to some other interactions involving Doves.
- MeSH
- biologická evoluce MeSH
- biologické modely MeSH
- časové faktory MeSH
- interpersonální vztahy * MeSH
- lidé MeSH
- teorie her * MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Dyadic interactions often involve a dynamic process of mutual reciprocity; to steer a series of exchanges towards a desired outcome, both interactants must adapt their own behaviour according to that of their interaction partner. Understanding the brain processes behind such bidirectional reciprocity is therefore central to social neuroscience, but this requires measurement of both individuals' brains during real-world exchanges. We achieved this by performing functional magnetic resonance imaging (fMRI) on pairs of male individuals simultaneously while they interacted in a modified iterated Ultimatum Game (iUG). In this modification, both players could express their intent and maximise their own monetary gain by reciprocating their partner's behaviour - they could promote generosity through cooperation and/or discourage unfair play with retaliation. By developing a novel model of reciprocity adapted from behavioural economics, we then show that each player's choices can be predicted accurately by estimating expected utility (EU) not only in terms of immediate payoff, but also as a reaction to their opponent's prior behaviour. Finally, for the first time we reveal that brain signals implicated in social decision making are modulated by these estimates of EU, and become correlated more strongly between interacting players who reciprocate one another.
- MeSH
- behaviorální ekonomie * MeSH
- dospělí MeSH
- interpersonální vztahy * MeSH
- kooperační chování MeSH
- lidé MeSH
- magnetická rezonanční tomografie metody MeSH
- mapování mozku metody MeSH
- mladý dospělý MeSH
- mozek fyziologie MeSH
- rozhodování * MeSH
- teorie her * MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- mladý dospělý MeSH
- mužské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Game theoretic models of evolution such as the Hawk-Dove game assume that individuals gain fitness (which is a proxy of the per capita population growth rate) in pair-wise contests only. These models assume that the equilibrium distribution of phenotypes involved (e.g., Hawks and Doves) in the population is given by the Hardy-Weinberg law, which is based on instantaneous, random pair formation. On the other hand, models of population dynamics do not consider pairs, newborns are produced by singles, and interactions between phenotypes or species are described by the mass action principle. This article links game theoretic and population approaches. It shows that combining distribution dynamics with population dynamics can lead to stable coexistence of Hawk and Dove population numbers in models that do not assume a priori that fitness is negative density dependent. Our analysis shows clearly that the interior Nash equilibrium of the Hawk and Dove model depends both on population size and on interaction times between different phenotypes in the population. This raises the question of the applicability of classic evolutionary game theory that requires all interactions take the same amount of time and that all single individuals have the same payoff per unit of time, to real populations. Furthermore, by separating individual fitness into birth and death effects on singles and pairs, it is shown that stable coexistence in these models depends on the time-scale of the distribution dynamics relative to the population dynamics. When explicit density-dependent fitness is included through competition over a limited resource, the combined dynamics of the Hawk-Dove model often lead to Dove extinction no matter how costly fighting is for Hawk pairs.
Příspěvek pojednává o kvalitativním výzkumu aplikačního vztahu dvou odlišných systémů – artefiletiky (art-philetic approach) a metody PRVA (Phenomenological Reflection of Visual Artifact), jejichž společnou podstatou je reflexe vizuálního díla se salutogenetickými cíli. Metodou kvalitativní evaluace bylo provedeno hodnocení tří reflektivních procesů: artefiletického (AP) a dvou experimentálních – EP1 a EP2 s včleněním metody PRVA. Výzkum byl proveden na dvou nezávislých souborech n=2 a n=2, vybraných prostým účelovým výběrem. Reflektivní procesy byly hodnoceny z hlediska způsobu realizace, atraktivity a smyslu pro participanty, motivačního potenciálu a vůle participantů k setrvání v procesu až do jeho ukončení. Cílem výzkumu je porozumění aplikačnímu vztahu mezi AP a PRVA s perspektivami hybridního procesu. Výsledky evaluací ukázaly, že vztah obou procesů je komplementární a jejich propojení je smysluplné a pozitivně produktivní pouze v pořadí „expresivní hra – reflektivní dialog – PRVA“.
This study deals with qualitative research of the application relationship between two distinct systems: art-philetic approach and Phenomenological Reflection of Visual Artifact (PRVA) method, whose common nature is the reflection of visual art with salutogenetic objectives. Qualitative evaluation method was used for evaluation of three reflective processes: art-philetic (AP) and two experimental – EP1 and EP2 while integrating PRVA method into AP. The research was carried out with two independent groups n=2 and n=2, chosen by the method of purposive sample. Reflective processes were assessed for the manner of realization, attractiveness and meaning, motivational potential and the will of participants to remain in the process until the end. The objective of the research is the understanding of the application relationship between AP and PRVA with perspectives of a hybrid process. The results have shown that the relationship between both processes is complementary and their interconnection is meaningful and positively productive only in the order: expressive game – reflective dialogue – PRVA.
- Klíčová slova
- artefiletika, metoda PRVA, kvalitativní evaluace, reflektivní dialog, salutogeneze,
- MeSH
- arteterapie * metody MeSH
- emoce klasifikace MeSH
- experimentální hry MeSH
- lidé MeSH
- mladiství MeSH
- psychologická teorie MeSH
- psychoterapie metody MeSH
- sebepojetí MeSH
- Check Tag
- lidé MeSH
- mladiství MeSH
- mužské pohlaví MeSH
- ženské pohlaví MeSH
Předkládaná stať si klade za cíl stručně seznámit čtenáře s hlavními myšlenkami a základními kame-ny teorie motorického učení OPTIMAL Gabriele Wulf a Rebeccy Lewthwait a poukázat na možnosti jejího využití ve školní tělesné výchově zejména při výuce sportovních her. Autorky kriticky pohlíží na „tradiční“ výuku nových pohybových dovedností a zdůrazňují časté opomíjení vnitřní motivace žáků a podporu jejich autonomie. Podle nich je žákům při tradičním vedení výuky vnucováno vnitřní zaměření pozornosti, tedy soustředění na pohyby těla či jeho částí. Uvádějí, že důsledkem takového přístupu je učení, které není dostatečně efektivní. Doporučují tedy pedagogům naopak vědomě zvyšo-vat očekávání žáků, podporovat potřebu autonomie jejich aktivnějším zapojením v učebním procesu a zaměřit pozornost vně směrem k cílům úkolu. Zdá se, že praktické využití teorie OPTIMAL ve školní tělesné výchově je možné. Především podporou autonomie sleduje aktuální trendy. Očekáváme však vysoké nároky kladené na organizaci učebního procesu i na pedagogy samotné. Je třeba teorii ještě v budoucnu testovat ve školní praxi. Ve sportovních hrách se již řadu let úspěšně užívá didaktické pa-radigma TGFU (Teaching Games for Understanding). Vzhledem k podobnosti některých principů teorie OPTIMAL a tohoto paradigmatu se jeví, že by i nová teorie motorického učení mohla být zejména při výuce základů herních dovedností ve sportovních hrách úspěšná. I to by však mělo být v budoucnu předmětem testován.
The objectives of the prepared article are to give the readers a brief account of the main ideas and foundations stones of a relatively new theory of motor learning, OPTIMAL, formulated by Gabriele Wulf and Rebecca Lewthwait, and also to point out the possibility of its application in school physical education lessons, particularly in teaching sports games. The authors critically assess “traditional” teaching of new locomotor skills stressing the frequent neglect of the internal motivation of pupils and support for their autonomy. According to them, in traditional teaching practice, internal focus of attention is imposed on the pupils, i.e. concentration on the movements of the body or its parts. They claim that the result of such an approach is learning that is not sufficiently effective. On the contrary, they recommend that the teachers should consciously raise the pupils’ expectations, support the need for autonomy by their more active involvement in the teaching process and focus their attention externally, towards the goals of the task. It seems that the practical application of the OPTIMAL theory in school physical education lessons is feasible. It is, above, all the support for autonomy that follows the current trends. However, we expect high demands set on the organization of the teaching process and on the teachers themselves. Future testing in the school practice is necessary. The TGFU (Teaching Games for Understanding) didactic paradigm has been successfully used in teaching sports games for a number of years. Due to the similarity of some principles of the OPTIMAL theory and this paradigm, it is apparent that the new theory of motor learning could be successful, too, particularly in teaching the fundamentals of game skills in sports games. This assumption, however, should also become a subject of testing in the future.
The theoretical and experimental research on opting out (also called conditional dissociation) in social dilemmas has concentrated on the effect this behavior has on the level of cooperation when used against defectors. The intuition behind this emphasis is based on the common property of social dilemmas that individuals are worse off the more their opponents defect. However, this article shows clearly that other opting out mechanisms are better at increasing cooperative behavior. In fact, by analyzing the stable Nash equilibria for the repeated multi-player public goods game with opting out, our results provide a strong argument that the best opting out rule is one whereby the only groups that voluntarily stay together between rounds are those that are homogeneous (i.e., those groups that are either all cooperators or all defectors), when these groups stay together for enough rounds. This outcome emerges when defectors are completely intolerant of individuals who cooperate (e.g., defectors exhibit xenophobic behavior toward cooperators) and so opt out whenever their group has a cooperator in it. The strong preference by defectors to be with like-minded individuals causes all heterogeneous groups to disband after one round.
- MeSH
- interpersonální vztahy MeSH
- kooperační chování * MeSH
- lidé MeSH
- rekreační hry MeSH
- skupinové procesy MeSH
- teoretické modely MeSH
- teorie her * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH