# Summary Games and Information An Introduction to Game Theory

ISBN-10 1405136669 ISBN-13 9781405136662
226 Flashcards & Notes
2 Students

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• ## 1.1 Definitions

• What are the essential elements of a game?
players, actions, payoﬀs, andinformation— PAPI
• Describe nature
Nature is a pseudo-player who takes random actions at speciﬁed points in the game with speciﬁed probabilities.
• ## 1.2 Dominated and dominated strategies: the prisoners dilemma

• Describe a dominated strategy
The strategy sd i is a dominated strategy if it is strictly inferior to some other strategy no matter what strategies the other players choose, in the sense that whatever strategies they pick, his payoﬀ is lower with s
• Describe a dominant strategy
The strategy s∗ i is a dominant strategy if it is a player’s strictly best response to any strategies the other players might pick, in the sense that whatever strategies they pick, his payoﬀ is highest with s∗
• Describe the prisoners dilemma
Whenever you observe individuals in a conﬂict that hurts them all, your ﬁrst thought should be of the Prisoner’s Dilemma.
• Describe a cooperative game
A cooperative game is a game in which the players can make binding commitments, as opposed to anoncooperative game, in which they cannot.
• ## 1.3 Iterated dominance: the battle of the bismarck see

• Describe a weakly dominated strategy
Strategy s0 i is weakly dominated if there exists some other strategy s00 i for player i which is possibly better and never worse, yielding a higher payoﬀ in some strategy proﬁle and never yielding a lower payoﬀ.
• Describe an iterated dominance equilibrium
An iterated dominance equilibrium is a strategy pro ﬁle found by deleting a weakly dominated strategy from the strategy set of one of the players, recalculating to ﬁnd which remaining strategies are weakly dominated, deleting one of them, and continuing the process until only one strategy remains for each player.
• Describe a zero-sum game
A zero-sum game is a game in which the sum of the payoﬀs of all the players is zero whatever strategies they choose. A game which is not zero-sum is nonzero-sum game or variable- sum.
• ## 1.4 Nash equilibrium

• When is there a nash equilibrium
The strategy pro ﬁle s∗ is a Nash equilibrium if no player has incentive to deviate from his strategy given that the other players do not deviate.
• Describe a battle of the sexes game
The third game we will use to illustrate Nash equilibrium is the Battle of the Sexes, a conﬂict between a man who wants to go to a prizeﬁght and a woman who wants to go to a ballet. While selﬁsh, they are deeply in love, and would, if necessary, sacriﬁce their preferences to be with each other.
• Describe the coordination game
coordination games, which share the common feature that the players need to coordinate on one of multiple Nash equilibria. Ranked Coordination has the additional feature that the equilibria can be pareto ranked.
• ## 2.1 The strategic and extensive form of a game

• The strategic or normal form consists of:
All possible strategy profiles
payoff function mapping
• ## 2.3 perfect, certain, symmetric and complete information

• Describe a perfect game
Each information set is a singleton
• Describe a certain game
Nature does not move first after any players moves
• Describe a symmetric game
No player has information different from other players when he moves, or at the end nodes
• Describe a complete game
Nature does not move first or her initial move is observed by every player
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Read Akerlof & Kranton’s article on “Economics of Identity”. What are the main assumptions the authors make regarding the factors that affect a person’s utility function? Use the example of “gender identity” to explain the factors.
Social categories, C (each person has a conception of her own categories cj and that of all other people)
Prescriptions P (behaviour appropriate for people in different social categories)
Identity: Social status of a category is given by the self-image Ij(·), Identity depends on
• the extent to which j’s own given characteristics ej match the ideal of j’s assigned category, indicated by the prescriptions P.
• the extent to which j’s own and others’ actions correspond to prescribed behaviour indicated by P.
According to Motivation Crowding Theory, what are the two effects of an external intervention on performance in an principal-agent relationship? Explain.
The relative price effect: Following the standard economic principal agent theory, external interventions impose a higher marginal cost on shirking, or increase the marginal monetary benefit of performing.  The crowding effect: all interventions originating from outside the person under consideration, i.e. both positive monetary rewards and regulations accompanied by negative sanctions may affect intrinsic motivation (marginal intrinsic benefit of performing).
Read Fehr et al., “Does fairness prevent market clearing?” Which type of efficiency wage theory is tested in this article? Describe the experiment and the main results.
Gift-exchange efficiency wages (here called ‘fair wage’ hypothesis). It is measures whether a ‘gift’ of a high wage is reciprocated by the worker by exerting higher effort. The experiment is an auction during a time of unemployment (so employers do not have to offer higher wages in order to attract workers). Employers offer higher than equilibrium wages and workers react by putting in more effort.
Shirking can be a large problem for employers. Instead of implementing monetary incentives like flexible wage schemes  also directly regulating employees can offer a solution for this. In “Shirking or work morale? The impact of regulating“ Frey warns, however, that there are possible negative effect of such regulation. Describe under which conditions this negative effect will appear.
Partly overlapping answer with question 1: Frey argues that monitoring has positive effects on the amount of output of the ‘rightly’ monitored workers. However, there might be a counteracting effect on those workers who feel that they need not be monitored: it signals that the principal does not know their real production/commitment. It might be that these workers feel discouraged to perform better than the minimum standard (the principal did not notice that they were doing more, anyway).
Read Frey’s “Motivation as a limit to pricing” and explain the title. How could (problems with) motivation limit the possibilities of pricing?
The answer to this is the summary of the entire article. Pricing (monetary incentives like flexible wage schemes) can lead to crowding out of intrinsic motivation. That may result in workers adjusting their level of effort downwards (crowding out of intrinsic motivation) if they feel that their efforts are not recognized by the employer or if they feel that the monetary incentives are unfair or if they feel that the control that they have over their own work is taken away from them
What is meant by “nudging” when used in economics?
This was originally defined by Richard Thaler and Cass Sunstein in their book “Nudge” as:“A nudge, as we will use the term, is any aspect of the choice architecture that alters people’s behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.”
If consumers have nonstandard preferences and beliefs, why should one expect firms, employers, financial operators, and politicians to not have them?
Experience is a key difference. Unlike individual consumers, firms can specialize, hire consultants, and obtain feedback from large data sets and capital markets. Firms are also subject to competition. Compared to consumers, therefore, firms are less likely to be affected by biases and we expect them to be close to profit maximization. (DellaVigna p.361)
What does DellaVigna expect with respect to the relationship between Psychology and Economics (i.e. Behavioural Economics) on the one hand and mainstream economics on the other hand?
) DellaVigna expects that the deviations from the standard model, as documented by Psychology and Economics (i.e. Behavioural Economics), will be increasingly incorporated into mainstream economics.
For which class of economic laboratory experiments could the results on behaviour more readily be extrapolated to the real world?
Experiments that do not trade-off morality and wealth, i.e. where there is no inherent conflict between moral choice and the wealth maximizing choice caused by scrutiny.  E.g. certain experiments exploring general economic theory, Bayesian updating, risk and uncertainty, psychological phenomena such as loss aversion, hyperbolic discounting, impersonal auctions, market experiments where the demand and cost functions are unknown—many of the above concerns, such as scrutiny effects, become inconsequential.
What factor(s) influence pro-social behaviour in experiments, and in which settings is it likely that pro-social actions are understated?
• 1) the presence of moral and ethical considerations; 2) the nature and extent of scrutiny of one's actions by others; 3) the context in which the decision is embedded; 4) self-selection of the individuals making the decisions; and 5) the stakes of the game.