Peace war game
Encyclopedia
An iterated game originally played in academic groups and by computer simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
for years to study possible strategies of cooperation
Cooperation
Cooperation or co-operation is the process of working or acting together. In its simplest form it involves things working in harmony, side by side, while in its more complicated forms, it can involve something as complex as the inner workings of a human being or even the social patterns of a...
and aggression
Aggression
In psychology, as well as other social and behavioral sciences, aggression refers to behavior between members of the same species that is intended to cause humiliation, pain, or harm. Ferguson and Beaver defined aggressive behavior as "Behavior which is intended to increase the social dominance of...
. As peace makers became richer over time it became clear that making war had greater costs than initially anticipated. The only strategy
Strategy
Strategy, a word of military origin, refers to a plan of action designed to achieve a particular goal. In military usage strategy is distinct from tactics, which are concerned with the conduct of an engagement, while strategy is concerned with how different engagements are linked...
that acquired wealth more rapidly was a "Genghis Khan
Genghis Khan
Genghis Khan , born Temujin and occasionally known by his temple name Taizu , was the founder and Great Khan of the Mongol Empire, which became the largest contiguous empire in history after his death....
", a constant aggressor making war continually to gain resources. This led to the development of the "provokable nice guy" strategy
Strategy
Strategy, a word of military origin, refers to a plan of action designed to achieve a particular goal. In military usage strategy is distinct from tactics, which are concerned with the conduct of an engagement, while strategy is concerned with how different engagements are linked...
, a peace-maker until attacked. Multiple players continue to gain wealth cooperating with each other while bleeding the constant aggressor. Such actions led in essence to the development of the Hanseatic League
Hanseatic League
The Hanseatic League was an economic alliance of trading cities and their merchant guilds that dominated trade along the coast of Northern Europe...
for trade and mutual defense following centuries of Viking
Viking
The term Viking is customarily used to refer to the Norse explorers, warriors, merchants, and pirates who raided, traded, explored and settled in wide areas of Europe, Asia and the North Atlantic islands from the late 8th to the mid-11th century.These Norsemen used their famed longships to...
depredation.
Cooperation
Cooperation or co-operation is the process of working or acting together. In its simplest form it involves things working in harmony, side by side, while in its more complicated forms, it can involve something as complex as the inner workings of a human being or even the social patterns of a...
, Defect
Defection
In politics, a defector is a person who gives up allegiance to one state or political entity in exchange for allegiance to another. More broadly, it involves abandoning a person, cause or doctrine to whom or to which one is bound by some tie, as of allegiance or duty.This term is also applied,...
) are replaced by (Peace
Peace
Peace is a state of harmony characterized by the lack of violent conflict. Commonly understood as the absence of hostility, peace also suggests the existence of healthy or newly healed interpersonal or international relationships, prosperity in matters of social or economic welfare, the...
, War
War
War is a state of organized, armed, and often prolonged conflict carried on between states, nations, or other parties typified by extreme aggression, social disruption, and usually high mortality. War should be understood as an actual, intentional and widespread armed conflict between political...
). Strategies remain the same with reciprocal altruism
Reciprocal altruism
In evolutionary biology, reciprocal altruism is a behaviour whereby an organism acts in a manner that temporarily reduces its fitness while increasing another organism's fitness, with the expectation that the other organism will act in a similar manner at a later time...
, "Tit for Tat
Tit for tat
Tit for tat is an English saying meaning "equivalent retaliation". It is also a highly effective strategy in game theory for the iterated prisoner's dilemma. It was first introduced by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. An agent using this strategy will initially...
", or "provokable nice guy" as the best deterministic
Deterministic algorithm
In computer science, a deterministic algorithm is an algorithm which, in informal terms, behaves predictably. Given a particular input, it will always produce the same output, and the underlying machine will always pass through the same sequence of states...
one. This strategy is simply to make peace on the first iteration of the game
Game
A game is structured playing, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements...
; after that, the player does what his opponent did on the previous move. A slightly better strategy is "Tit for Tat with forgiveness". When the opponent makes war, on the next move, the player sometimes makes peace anyway, with a small probability. This allows an escape from wasting cycles of retribution, a motivation similar to the Rule of Ko in the game of Go
Go (board game)
Go , is an ancient board game for two players that originated in China more than 2,000 years ago...
. "Tit for Tat with forgiveness" is best when miscommunication is introduced, when one's move is incorrectly reported to the opponent. A typical payoff matrix for two players (A, B) of one iteration of this game
Game
A game is structured playing, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements...
is:
Peace
Peace is a state of harmony characterized by the lack of violent conflict. Commonly understood as the absence of hostility, peace also suggests the existence of healthy or newly healed interpersonal or international relationships, prosperity in matters of social or economic welfare, the...
War
War is a state of organized, armed, and often prolonged conflict carried on between states, nations, or other parties typified by extreme aggression, social disruption, and usually high mortality. War should be understood as an actual, intentional and widespread armed conflict between political...
Peace
Peace is a state of harmony characterized by the lack of violent conflict. Commonly understood as the absence of hostility, peace also suggests the existence of healthy or newly healed interpersonal or international relationships, prosperity in matters of social or economic welfare, the...
War
War is a state of organized, armed, and often prolonged conflict carried on between states, nations, or other parties typified by extreme aggression, social disruption, and usually high mortality. War should be understood as an actual, intentional and widespread armed conflict between political...
Here a player's resources have a value of 2, half of which must be spent to wage war. In this case, there exists a Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
, a mutually best response for a single iteration, here (War, War), by definition heedless of consequences in later iterations. "Provokable nice guy's" optimality
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
depends on iterations. How many are necessary is likely tied to the payoff matrix and probabilities of choosing. A subgame perfect version of this strategy is "Contrite Tit-for-Tat" which is to make peace unless one is in "good standing" and one's opponent is not. Good ("standing" assumed) means to make peace with good opponents, make peace when bad, or make war when good and opponent is not.