Chapter 2. Research Design and Methodology 2.1. Introduction
2.2 Game Theory and Realism: absolute gains, relative gains, and the zero-sum
2.2.3 Rational Choice & Game Theory
2.2.3.1 Game Theory Concepts 3
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Rational Choice can be defined has the optimum strategy for one actor to a given
competitive situation. Game theory is the process through one actor decides his
optimum strategy, normally, under conditions of uncertainty and incomplete
information. Each actor has to rank order preferences, estimate probabilities, and try
to find out what the other actor is going to do (Viotti, & Kauppi, 2010).
2.2.3.1 Game Theory Concepts3
This section introduces the basic game theory concepts that are applied during the
case study in SCS.
The Rules of the game
When we talk about games in this theory, we refer to those simplified representations
of strategic situations that can be found in different fields of human life (business,
politics, diplomacy, military, etc.). These games have basic common characteristics:
- The list of the players
3 Unless otherwise specified, based on: Dixit, Avinash K. & Susan Skeath. Games of Strategy.
New York: Norton, 1999.
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- The strategies available for each player’s actions
- The payoffs from all the possible combinations of strategies
- All players are considered rational maximizers.
They can be represented, for instance, in a game table like the famous prisoner’s
dilemma game (Table 1). In the case of this game, two suspects for committing a
crime that are in different cells are told separately (without knowing the other’s
decision) that if one confesses who did the crime, he will be freed but his partner will
expend four years in prison. Otherwise, if both confess they will expend three years in
prison, and finally, if both stay quiet they will expend only one year in prison
(Osborne, 2009, p.14-15).
Table 1. Prisoners' dilemma Game. Payoffs in level of preference.
List of players: suspect 1, suspect 2 Strategies available: quiet, fink
Payoffs: 0, 1, 2, 3 (level of preference: 0 is the worse outcome, 3 is the best one) Players are rational maximizer: want to expend the less time possible in prison.
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Types of game according to player’s movement order
There are two types of games according to the order of strategic movements:
sequential and simultaneous games.
In sequential games, there is an order of play in which players take turns to move,
and each knows the movements made by the previous player. These games are usually
represented in games trees (see Figure 1), which is also called the extensive form of
a game.
China
altruistic selfish
Disputants Disputants
altruistic selfish altruistic selfish 4, 4 1, 3 3, 1 2, 2
Figure 1. Game in tree form
In simultaneous games, players must move without knowing what the other players
have chosen to do and cannot change its action. These games are represented in a
game table (see the previous prisoners’ dilemma example, Table 1), which is the
strategic form of a game.
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Types of equilibrium
Equilibrium means that each player is using a strategy that is the best response to
other players’ strategies. Depending on if the game is sequential or simultaneous, the
equilibrium can be found by:
- Rollback Equilibrium: occurs in games with sequential movements. It is reached
using the rollback methodology, which implies to think what happen in the
terminal nodes of the game tree, and go back through the branches, decision node
by decision node until reaching the initial node, reasoning which combination of
players’ strategies leads to the equilibrium.
- Nash Equilibrium: occurs in games with simultaneous movements. In these kind
of games we cannot use rollback, thus we have to find a configuration of
strategies that makes each player’s strategy it best choice when other players also
use their equilibrium strategy. It can be identified using different ways: with
dominant strategies, eliminating dominated strategies, minimax strategy, or cell by
cell inspection.
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Cooperative and Non-Cooperative Games
The terminology in game theory can cause some confusion due to the concept of
cooperative is not equal to cooperation. Avinash and Skeath (1999), define
cooperative games as follow:
- Cooperative games: are those games in which the enforcement of a joint
agreement is possible, perhaps because it is enforced with all the members at the
moment of the sign, or because the players are monitored by a third party that can
enforce the agreement.
- Non-Cooperative games: are those games in which the enforcement is not
possible, and thus individuals can act in their own interests.
Although their names make to think the opposite, even the non-cooperative type allow
for cooperation in the case of repeated interactions between the players, and if it is on
each player own interests to take the cooperative action during the indefinite numbers
of interactions (see: the Shadow of the Future).
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The Shadow of the Future
This idea for initiate cooperation in non-cooperative games like prisoner’s dilemma is
part of the concept the Shadow of the Future, an expression which means that next
encounter between the same two players must be important enough to make the
unwillingness to cooperate unprofitable. This happens when players do not know how
more times are they going to interact, thus, when the shadow of the future is long
enough to hide the remaining number of interactions, the payoff for cooperation are
bigger than for noncooperation (Axelrod, 1984, p.174).
Collective Action Games
These kind of games are those in which the aim of the collective (society, group of
countries, group of players, etc.), are best achieved if they take an specific action or
actions, even when these actions are not in the best personal interests of those players.
This implies that the collective optimal outcome is not the Nash equilibrium of the
game, and thus, the game will not automatically end in this optimal situation. In order
to achieve this ideal situation, we need to understand the essence of the game, the
players’ system values (that they are rational do not imply that always have the same
values), and how can we modify it to obtain the optimal outcome for the collective
group.
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Some characteristic of collective actions games are the followings:
- Non-excludable: a player who has not contributed to the support of an specific
plan of action (e.g. establishing a common vigilance patrol in a neighbors
community, establishing join security patrols in SCS, etc.), cannot be prevented
from getting the benefits.
- Non-rival: a player’s benefits are not diminishing because others players are also
obtaining the benefit (e.g. the patrols provide security to all the
community/region).
- Pure public good: refer to those goods that possess non-excludable and non-rival
characteristics (e.g. a public park in the city).
- Pure private good: refer to those goods in which non-players can be excluded
from their benefits. Moreover, if one actor obtains the benefit, no other actor can
enjoy them (e.g. a cold pill). Normally, goods are in between the
excludable/non-excludable and rival/non-rival spectrum.
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The Importance of a Focal Point
This refers to an outcome in which all players understand that, among all the possible
equilibria of the game, the focal point is the obvious to choose. All players’
expectations must converge to that point, which means that all actors consider that
equilibrium as the one which provide them with better payoffs. This easily happens in
assurance games, where one of the equilibria have higher payoff for both of the
players. However, in some occasions there is other equilibrium which worse payoffs
for the players but less risky due to it is the best response for all the participants
independently what other players’ strategies are (see for instance table 2. US and
U.S.S.R. arm race). In other cases can be difficult make players to converge their
expectations on the same focal point, mainly because is more a matter of player’s
backgrounds, history, culture, norms of behavior between groups, etc., than a question
of mathematics (Dixit & Skeath, 1999). Therefore, in some occasions it is necessary
to make strategic moves in order to modify the rules of the game, leading the
opponent to make decisions that favors our preferred outcome (e.g. the focal point).
Strategic moves
Sometimes, a player may try to shape the game is playing to compel or deter other
player to take a specific action in the moment he has to choose his strategy during a
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sequential game. Those devices used to manipulate the rules of the game are called
strategic moves. They highly depend on the order of moves in which, in the case of
the player with the initiative (the one who move first), the action must be observable
to the other player, and must be irreversible, that is, cannot be changed it in a later
point of the game.
Strategic moves modify the rules of the original game to create a new game with two
stages. In the first stage the player indicate how he will act (which strategy he is
going to use) during the second stage. The second stage is the original game,
normally with some modification of the payoffs and the order of moves.
During the first stage a player can make three different strategic moves: commitments,
threats, and promises:
- Commitments refer to a declaration made by a player A indicating that its future
movement in stage two is unconditional. For instance, player A can say “I will do
X in the game we are playing”, and during the second stage he will do X
independently of player B’s strategy.
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In the cases of threats and promises, they belong to the category of response rules,
statements made by one player that indicate his future response to other player’s
specific actions during stage two.
- Threats are response rules that try to deter the other player to choose a specific
strategy. Player A can say “If you choose X that annoys me, I will do Y (e.g. I will
hurt you)”.
- Promises are response rules that try to compel the other player to choose a
specific strategy. Player A can say “If you do Z that pleases me, I will do W (e.g. I
will reward you)”.
These strategic moves only work if the other player believes that the first player will
do what he announced at the first stage, which makes credibility an important factor
for the effectiveness of the strategic movement, and thus, has to be taken into account.
Types of collective action games
These games appear in three different types: prisoners’ dilemma, chicken games, and
assurance games. In this research we focus only in assurances games as we consider
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is the one who better describe the theoretical framework for SLOCs cooperation in
SCS, as we will explain in the case study section.
- Assurance Games
Assurance games are those that have two or more possible equilibria in a single game.
It may involve no conflict in payoffs among the players participating in the game, and
thus all the players will prefer the same equilibrium.
A clear example is the US and U.S.S.R arms races during the Cold War (Table 2), in
which both superpowers had two strategies, to cooperate to avoid weapons build up
or to defect. Both countries are interested in deprived the other actor from defect, and
may sacrifice defection ability if others do the same. Thus the table for this game will
be as follow (Jervis, 1978)4:
Table 2. Arms Race Game
4 Table modified from the original to show payoffs instead of order of the actors’ preferences.
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