4.1: Social Interactions – Game Theory:
Terminology:
1) Social Dilemma = this occurs when we don’t take account of how our own personal
decisions (e.g. consumption) impact on other people’s wellbeing (or utility)
2) The Tragedy of the Commons = this occurs when a resource isn’t owned by anyone
in particular, it is easily overexploited and degraded when individuals act selfishly,
unless you control access in some way.
3) Strategic Interaction = when people are engaged in a social interaction, and are
aware of the ways in which their actions affect others, and vice versa
4) Strategy = a complete plan of action which describes the actions that an individual
will take throughout the course of the interaction
5) Games = models of strategic interactions and consist of players, feasible strategies,
payoffs (numerical outcome) and information
6) Game Theory = the study of these strategic interactions, which is widely used in
economics, biology, mathematics and other social sciences.
7) Simultaneous move game = move with same information e.g. rock, paper, scissors
8) Sequential move game = move one after the other after processing previous
information e.g. chess
9) Nash Equilibrium = the combination of strategies in a game such that neither player
has an incentive to change their strategies, given the strategy choice of their opponent
(mutual best response)
10) Dominant Strategy = sometimes there is one strategy which always provides a
player with a higher payoff, no matter what the other player does.
11) Dominant strategy equilibrium: An outcome of a game in which every player plays
his or her dominant strategy.
12) Zero-sum game: The players’ interests are in direct conflict with one another. For
example, in football, one team wins and the other team loses. If a win equals +1 and a
loss equals -1, the sum is zero
13) Non-zero sum game: The players’ interests are not always in direct conflict, so that
there are opportunities for both to gain. For example, when both players choose
“don’t confess” in Prisoner’s Dilemma (see below).
14) One-shot games: The play of the game occurs only once. Here, the players are likely
to not know much about each other. For example, tipping a waiter on your vacation
15) Repeated games: The play of the game is repeated with the same players.
16) Invisible Hand Game = whereby the NE is also the socially optimal outcome
without any interaction/prior information being given
17) Prisoners’ Dilemma = is one which exhibits: both players have a dominant strategy
& would do better in the outcome where they play their non-dominant strategy (also
called the dominated strategy) than they do in the Nash Equilibrium
18) Assurance game = where there are two Nash Equilibria where
both players play the same strategy, but both players strictly prefer
one Nash Equilibrium over the other. This game exhibits
multiple equilibria.
19) Battle of the sexes game = where there are two Nash Equilibria
where both players play the same strategy, but players prefer
different equilibria. This game exhibits conflicting equilibria.
, 4.2: Equilibrium in the Invisible Hand Game:
Basic Game and Solving for the Nash Equilibrium:
• NB! Use the Best Response Method!
• NE = (Sugar Cane, Maize)
• The Nash Equilibrium Outcome (NEO) is the payoffs
associated with the Nash Equilibrium [NEO = (4, 4)]
• The NE is a dominant strategy equilibrium, as both
players are playing their dominant strategy
How to solve:
• To predict the outcome of a game, we need another concept: best response.
• This is the strategy that will give a player the highest payoff, given the strategies the
other players select i.e. if Betty plays Mazie, then holding this strategy constant,
which strategy will Amandla play? She will play Sugar Cane as a payoff of 4 is
greater than a playoff of 1.
• We can represent players payoffs using a standard format called a payoff matrix. The
first number in each box is the reward received by the row player. The second number
is the column player’s payoff.
Assumptions Game Theorists Make:
• The payoffs are known and fixed
• All players behave rationally
• The rules of the game are common knowledge.
Terminology:
1) Social Dilemma = this occurs when we don’t take account of how our own personal
decisions (e.g. consumption) impact on other people’s wellbeing (or utility)
2) The Tragedy of the Commons = this occurs when a resource isn’t owned by anyone
in particular, it is easily overexploited and degraded when individuals act selfishly,
unless you control access in some way.
3) Strategic Interaction = when people are engaged in a social interaction, and are
aware of the ways in which their actions affect others, and vice versa
4) Strategy = a complete plan of action which describes the actions that an individual
will take throughout the course of the interaction
5) Games = models of strategic interactions and consist of players, feasible strategies,
payoffs (numerical outcome) and information
6) Game Theory = the study of these strategic interactions, which is widely used in
economics, biology, mathematics and other social sciences.
7) Simultaneous move game = move with same information e.g. rock, paper, scissors
8) Sequential move game = move one after the other after processing previous
information e.g. chess
9) Nash Equilibrium = the combination of strategies in a game such that neither player
has an incentive to change their strategies, given the strategy choice of their opponent
(mutual best response)
10) Dominant Strategy = sometimes there is one strategy which always provides a
player with a higher payoff, no matter what the other player does.
11) Dominant strategy equilibrium: An outcome of a game in which every player plays
his or her dominant strategy.
12) Zero-sum game: The players’ interests are in direct conflict with one another. For
example, in football, one team wins and the other team loses. If a win equals +1 and a
loss equals -1, the sum is zero
13) Non-zero sum game: The players’ interests are not always in direct conflict, so that
there are opportunities for both to gain. For example, when both players choose
“don’t confess” in Prisoner’s Dilemma (see below).
14) One-shot games: The play of the game occurs only once. Here, the players are likely
to not know much about each other. For example, tipping a waiter on your vacation
15) Repeated games: The play of the game is repeated with the same players.
16) Invisible Hand Game = whereby the NE is also the socially optimal outcome
without any interaction/prior information being given
17) Prisoners’ Dilemma = is one which exhibits: both players have a dominant strategy
& would do better in the outcome where they play their non-dominant strategy (also
called the dominated strategy) than they do in the Nash Equilibrium
18) Assurance game = where there are two Nash Equilibria where
both players play the same strategy, but both players strictly prefer
one Nash Equilibrium over the other. This game exhibits
multiple equilibria.
19) Battle of the sexes game = where there are two Nash Equilibria
where both players play the same strategy, but players prefer
different equilibria. This game exhibits conflicting equilibria.
, 4.2: Equilibrium in the Invisible Hand Game:
Basic Game and Solving for the Nash Equilibrium:
• NB! Use the Best Response Method!
• NE = (Sugar Cane, Maize)
• The Nash Equilibrium Outcome (NEO) is the payoffs
associated with the Nash Equilibrium [NEO = (4, 4)]
• The NE is a dominant strategy equilibrium, as both
players are playing their dominant strategy
How to solve:
• To predict the outcome of a game, we need another concept: best response.
• This is the strategy that will give a player the highest payoff, given the strategies the
other players select i.e. if Betty plays Mazie, then holding this strategy constant,
which strategy will Amandla play? She will play Sugar Cane as a payoff of 4 is
greater than a playoff of 1.
• We can represent players payoffs using a standard format called a payoff matrix. The
first number in each box is the reward received by the row player. The second number
is the column player’s payoff.
Assumptions Game Theorists Make:
• The payoffs are known and fixed
• All players behave rationally
• The rules of the game are common knowledge.
