Unit 5 Flashcards
What are institutions, incentives and power in game theory?
Institutions or rules are sets of laws that regulate social interaction. They affect how the game is likely to be played, the size of the total payoff and how the total is divided.
Incentives are the economic reward or punishment which influence the benefits and costs of alternative courses of action.
Power is the ability to do and get things we want in opposition to the intentions of others.
What are the two forms of power in game theory?
- Structural power: the value of the next best alternative. Two people will only strike a deal if it yields an outcome that is an improvement over what they could get if they ended the deal and pursued other alternatives. The ability to walk away from a bad deal is structural power.
- Bargaining power: structural power determines the most and least people can get from an interaction. What they actually get between the two extremities is determined by their bargaining power. A person exercising bargaining power may set the terms of an exchange, ie a take-it-or-leave-it offer, or threaten to impose heavy costs on the other to coerce behaviour
How can fairness be used to evaluate economic interactions and games?
Substantive judgements of fairness evaluate an outcome based only on its allocation. Ie a split of £99 and £1 in the ultimatum game is very unfair.
Procedural judgements of fairness evaluate an outcome based on how the allocation came about looking at the rules of the game. Ie forcing a 50-50 split by holding a gun at the other player is unfair.
How can substantive and procedural judgements be evaluated?
Substantive judgements are difficult to evaluate as they are subjective. Possible criteria include measuring financial wellbeing, freedom or happiness.
Procedural judgements can be evaluated via legitimacy of voluntary exchange (whether players’ actions were freely chosen), equal opportunity (whether race, gender, sex etc affected whether a player had equal opportunity to acquire a large share of the divided total) and deservingness (whether institutions considered how hard an individual worked or whether they upheld social norms).
Evaluate the ultimatum game using fairness.
The ultimatum game is procedurally fair as proposers are chosen at random, the game is played anonymously, discrimination isn’t possible and all actions are voluntary.
Whether the ultimatum game is substantively fair depends on the allocation itself. A 50-50 split is fair in most cases whilst a 90-10 is not.
What is the veil of ignorance, by John Rawls?
The veil of ignorance invites you to put yourself in the shoes of others to make a judgement about fairness. In the ultimatum game, we do not know whether we would be the proposer or responder, similarly in real life, we do not know what our sex, race, gender etc will be. As an impartial outsider who doesn’t know what their position will be, you can evaluate the institutions of society.
Outline a game between Angela and Bruno to evaluate how rules of the game affect power and outcomes.
Angela is a farmer working on Bruno’s land. The amount of grain farmed by Angela is owned by Bruno who decides how to divide it between the two. The grain is the income to both players.
Angela wants the best feasible combination of free time and grain.
Bruno wants as much grain as possible.
We assume the two are entirely self interested. Angela only values grain and free time.
Removing Bruno from the situation and considering a scenario where Angela owns the land and consumes alp the grain she produces, what combination of free time and grain would she choose?
As in previous units, we can draw Angela’s indifference curves for all combinations of both goods. Then we can add her feasible set of combinations. She will choose the combination on the indifference curve which is tangential to her feasible set, where MRS=MRT.
Consider the case where Bruno owns the land and can choose Angela’s free time and amount of grain through force. Angela’s only choices are to obey or revolt. What will Bruno choose?
Using Angela’s feasible set we can observe all possible combinations of free time and grain. Among these combinations, Bruno chooses the proportion of grain Angela will receive. Some of these combinations yield the same level of utility to Angela as revolting and risking death would, ie her reservation option. By joining these points, we form Angela’s reservation indifference curve.
The reservation indifference curve and original feasible set create a new feasible set representing the options bruno can choose that give Angela at least her reservation option utility without overworking/starving her or causing her to revolt.
Bruno will therefore choose the point on the reservation indifference curve that yields him the most grain. At this point, the reservation indifference curve has the same slope as the feasible frontier.
Consider a take it or leave it scenario whereby Bruno owns the land but the legal system ensures Bruno cannot force Angela to do work and must offer a contract, what outcome would occur?
- Bruno can offer an employment contract, specifying Angela’s hours of work and wage to which Angela can accept or reject. Using Angela’s feasible set and reservation indifference curve, Bruno will choose the point on the indifference curve which has the same slope as the feasible frontier, giving Bruno the largest amount of grain possible.
- Bruno can offer a tenancy contract whereby he specifies the rent Angela must pay him to use the land and she can choose how to use it, to which Angela can accept or reject. Bruno will choose to offer Angela her reservation utility and specify 23 bushels of grain - the same he would receive under an employment contract. Angela can choose her hours of work and so Angela’s feasible frontier for grain consumption is a curve that is, for all hours of free time, 23 bushels under her original feasible frontier. Angela will choose again 8 hours of work. These outcomes are the same as under the employment contract.
Why is Angela’s working hours always the same, whether she can choose her hours, Bruno chooses by force or she can accept via contract?
Angela’s MRS at a given level of hours is the same on every indifference curve. It is always the case that she and Bruno do best where MRS=MRT.
Assess the outcomes of the case where Bruno forces Angela into labour and the case where Bruno offers a contract.
In both cases, Angela’s working hours are the same and she receives her reservation utility (zero economic rent). But because Angela has better outside options when given a contract, her reservation utility is higher so she is better off in the second scenario and earns higher income.
Bruno is better off in the first scenario as he earns a higher rent as the rules of the game give him more structural power.
In both cases, Bruno has all the bargaining power. Both cases produce Pareto efficient outcomes as any alternative outcome would make one of them worse off.
What would the outcome be if Angela, amongst other farmers, votes to improve her working conditions?
If the government implement a policy stating maximum working hours and minimum pay for farmers, Bruno must offer a new contract in alignment with the policy.
Now, no matter how many hours Angela works, Bruno must pay her at least the minimum wage.
Therefore, Bruno would choose to offer Angela the lowest wage possible (minimum wage) and maximum hours as this maximises his payoff.
Angela’s reservation indifference curve shifts up. She is paid the minimum wage and still earns no economic rent but is better off as she has more free time.
Why is the outcome when Angela has democratic bargaining power not Pareto efficient?
The slope of her indifference curve is less than the slope of her feasible frontier. Therefore, MRS<MRT. Whenever MRS and MRT are unequal, there is room for a Pareto improvement which, in this case, would make Angela and Bruno better off.
What is the Pareto efficiency curve?
The set of all allocations that are Pareto efficient (MRS=MRT). When we assume one’s indifference curves are all parallel, the Pareto efficiency curve is a vertical line as for every indifference curve, MRS=MRT at the same x axis point.
What do the Angela and Bruno situations reveal to us about efficiency and fairness?
- When one person or group has power to dictate the allocation, subject only to not making the other person worse off than their reservation option, that person will capture the entire surplus. This outcome is Pareto efficient but likely unfair.
- if those who consider their outcome unfair have the power to influence the outcome through legislation and other political means, the result may be a fairer distribution but not Pareto efficient. Thus, societies can face trade offs between an outcome that is fair or Pareto efficient.
- this trade off can be avoided if we have institutions that allow people to discuss allocations and achieve both Pareto efficiency and fairness.
What does an individual’s income depend on?
- Their endowments (things they have that enable them to receive income), including financial wealth, physical assets, human capital, race, gender etc
- The income derived from each endowment
What is the Gini coefficient and how is it calculated?
The gini coefficient is a measure of inequality of a quantity such as income or wealth varying from a value of 0 (complete equality) to 1 (complete inequality).
The gini coefficient is one half multiplied by the average difference in income or wealth between every pair of individuals in the population divided by the average income of the population.
