Information, Uncertainty and Games

One of the assumptions of most welfare theorems is that the properties of all commodities are observable by all participants. But in reality, this is almost impossible. There are many variables about which we cannot obtain sufficient information. Information is asymmetrical to market participants. For example, we cannot know the exact quality of a product we are going to buy as well as the seller. We can only make assumptions about it. 

Expected Value is the sum of all possible outcomes weighted, where each possible value is weighted by its respective probability. Expected Utility (EU) is the expected value of utility over all possible outcomes.

A “fair game” is a random game with a given set of prizes and corresponding probabilities with an expected value of zero.

EV_w= (3/5)x(10x20000)+(2/5)x(10x5000)=140000

EV_r= (3/5)x(20x10000)+(2/5)x(20x2000)=136000

Risk averse is a person who refuses a gamble when the expected value is zero, therefore refuses fair gambles.

Risk seeking/ Risk taker, preferences described by a utility function with increasing marginal utility of wealth. Risk Neutral, preferences described by a utility function with constant marginal utility of wealth.

Risk Neutral, preferences described by a utility function with constant marginal utility of wealth. If a person is risk neutral, then that means she is indifferent between refusing or accepting the fair gamble and her utility function will have constant slope.

Adverse selection arises when an informed individual’s decisions in the market affects adversely uninformed market participations.

People take some cautions, like buying fire extinguishers for houses in case of a fire, for the probability that a risky event will occur. We know insurance is one of those cautions. But in the case of insurance, the attitudes of people might change. For example, if someone has car insurance then he or she might drive recklessly. Or if the insurance protects him/her against theft, then he/she might not be willing to install an alarm. This phenomenon is termed moral hazard. So, people who know their car, house etc. are covered by insurance may not take some precautions because these precautions are also costly.

Game theory is the theory that helps individuals to make better choices in more complicated situations. Game theory is a branch of applied mathematics that models’ situations where payoffs arise from players’ strategic interactions with each other.

In game Theory, a game is given by a mostly limited number of players interacting with each other according to certain given rules and it’s an abstract model of a strategic situation.

If a strategy always gives the player a better payoff, regardless of which strategies other players choose, that strategy dominates all other strategies of that player and is called dominant strategy.

In the game theory models, decision makers are called players. These players are dependent on each other for decision making. This means that each player must consider the strategies of the other player or players in the game. In each game, players have certain gains and losses that they get as a result of each decision they make, which we call payoff.

In the game theory models, decision makers are called players. These players can be individuals, groups, companies, associations, and the like. In a game in strategic form, every one of the given possible actions of a player is called strategy.

In game theory, games are basically evaluated under four main groups. This distinction is made as static games or dynamic games depending on the decision-making processes of the game, and games of incomplete information or complete information depending on the information that players have. These four main games are static games of complete information, static games of incomplete information, dynamic games of complete information and dynamic games of incomplete information.

In a game if the players choose their strategies simultaneously, it is called a static game, but if the game has an order of play, it is called a dynamic game. So, we can easily make the static-dynamic distinction in a game by examining whether the players choose their strategies simultaneously or not. In static games, players make their moves without observing the moves of other players. This does not mean that they decide the strategy that they will choose at the same time. It simply means that strategy decisions are played at the same time.

Dynamic games have an order of play, unlike static games. Players can observe each other’s moves as the game progresses. A game can be dynamic in two situations. First case; interaction between players can happen naturally, dynamically. In this way, players can observe each other’s moves. In the second case, if a one-time game is repeated several times, it becomes dynamic and the players who observe the result in the first game get information about the moves of the other players without playing the game in the next games.

Games in which players choose their strategies simultaneously and they have complete information are called static games of complete information.

Games in which players choose their strategies sequentially and they have complete information are called dynamic games of complete information. Games in which players choose their strategies sequentially and they have incomplete information are called dynamic games of incomplete information.

The Nash equilibrium concept is based on the best-response approach. A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for each player, which has the property that no player can unilaterally change his strategy and get a better payoff. In a Nash equilibrium, no player has incentive to change his/her current strategy.