Game theory fundamentals for product managers
Game theory fundamentals for product managers
“I use game theory to help myself understand conflict situations and opportunities.” — Thomas Schelling
Game Theory Definitions :
Game theory is the study of mathematical models of strategic interaction among rational decision-makers.
Any time we have a situation with two or more players that involve known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes. Let's start out by defining a few terms commonly used in the study of game theory:
Game: Any set of circumstances that has a result dependent on the actions of two or more decision-makers (players)
Players: A strategic decision-maker within the context of the game
Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game
Payoff: The payout a player receives from arriving at a particular outcome (The payout can be in any quantifiable form, from dollars to utility.)
Information set: The information available at a given point in the game (The term information set is most usually applied when the game has a sequential component.)
Equilibrium: The point in a game where both players have made their decisions and an outcome is reached
Game types
Cooperative / non-cooperative
A game is cooperative if the players are able to form binding commitments externally enforced (e.g. through contract law). A game is non-cooperative if players cannot form alliances or if all agreements need to be self-enforcing
Cooperative games are often analyzed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take, and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria
Cooperative game theory provides a high-level approach as it describes only the structure, strategies, and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation. While it would thus be optimal to have all games expressed under a non-cooperative framework, in many instances insufficient information is available to accurately model the formal procedures available during the strategic bargaining process, or the resulting model would be too complex to offer a practical tool in the real world. In such cases, cooperative game theory provides a simplified approach that allows analysis of the game at large without having to make any assumption about bargaining powers.
Symmetric / asymmetric
Asymmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. That is, if the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the commonly studied 2×2 games are symmetric. The standard representations of chicken, the prisoner's dilemma, and the stag hunt are all symmetric games. Some[who?] scholars would consider certain asymmetric games as examples of these games as well. However, the most common payoffs for each of these games are symmetric.
The most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the ultimatum game and similarly the dictator game have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.
Zero-sum / non-zero-sum
Zero-sum games are a special case of constant-sum games in which choices by players can neither increase nor decrease the available resources. In zero-sum games, the total benefit to all players in the game, for every combination of strategies, always adds to zero (more informally, a player benefits only at the equal expense of others).[15]Poker exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include matching pennies and most classical board games including Go and chess.
Many games studied by game theorists (including the famed prisoner's dilemma) are non-zero-sum games, because the outcome has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.
Constant-sum games correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential gains from trade. It is possible to transform any game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called "the board") whose losses compensate the players' net winnings.
Simultaneous / sequential
Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players' actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be perfect information about every action of earlier players; it might be very little knowledge. For instance, a player may know that an earlier player did not perform one particular action, while they do not know which of the other available actions the first player actually performed.
The difference between simultaneous and sequential games is captured in the different representations discussed above. Often, normal form is used to represent simultaneous games, while extensive form is used to represent sequential ones. The transformation of extensive to normal form is one way, meaning that multiple extensive form games correspond to the same normal form. Consequently, notions of equilibrium for simultaneous games are insufficient for reasoning about sequential games; see subgame perfection.
Theory of emotion
Plutchik proposed a psychoevolutionary classification approach for general emotional responses. He considered there to be eight primary emotions—anger, fear, sadness, disgust, surprise, anticipation, trust, and joy. Plutchik argues for the primacy of these emotions by showing each to be the trigger of behaviour with high survival value, such as the way fear inspires the fight-or-flight response.
Plutchik's psychoevolutionary theory of basic emotions has ten postulates.
The concept of emotion is applicable to all evolutionary levels and applies to all animals including humans.
Emotions have an evolutionary history and have evolved various forms of expression in different species.
Emotions served an adaptive role in helping organisms deal with key survival issues posed by the environment.
Despite different forms of expression of emotions in different species, there are certain common elements or prototype patterns, that can be identified.
There is a small number of basic, primary, or prototype emotions.
All other emotions are mixed or derivative states; that is, they occur as combinations, mixtures, or compounds of the primary emotions.
Primary emotions are hypothetical constructs or idealized states whose properties and characteristics can only be inferred from various kinds of evidence.
Primary emotions can be conceptualized in terms of pairs of polar opposites.
All emotions vary in their degree of similarity to one another.
Each emotion can exist in varying degrees of intensity or levels of arousal.
Emotions influence our actions in five main ways, which we outline here:
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Emotion Component
This is where an individual simply experiences the feelings. It’s about monitoring the internal universe and recognizing what is being experienced at that time.
Action Tendency Component
Once the emotion is identified, the body moves into action. Emotions bestow certain actions instead of others, which means that while some are beyond our control (and thankfully so), like pulling your hand away from a hot iron, others are within our control, facing the fear to continue with a speech or a presentation.
Appraisal Component
By cognitively analyzing the emotion, the individual is able to pick up on the situations, actions, environments, or individuals that are causing the emotion. This aids the individual in tracking how these stimuli impact their well-being. It’s also invaluable for helping communicate the state of our internal world with others.
Motor Component
This is the communicative function of how we express what we are experiencing (facial expressions, hand gestures, body movements, etc.). So it is extremely important on the inter-individual level, as well as that of the individual.
Physiological Component
This component supports all others and is the chemical reaction that our body experiences. For instance, the rush of blood flow to the hands occurs when one experiences the emotion of anger.
While the components of the emotions we feel are present in all individuals, the intensity and expression of these emotions differ from one person to another. There are also social factors like gender, culture, and race, that influence why people may feel emotions differently despite similar situations.