2. • Does the Mahabharat formulate the first example of ‘game theory’?
The Mahabharat begins with a game, which leads to a war and great
suffering before redemption is finally achieved. What is the message
of this? If we generally accept the Bhagavad Gita as an integral part of
the epic (though many claim it was a much later interpolation) we
might find a clue.
3. • Shakuni masterminds chaupar - a gambling game of dice
• The Kauravas possessed asymmetric information that the dice to be
used in the gambling game were rigged. Yudhishthir unwittingly made
an adverse selection and accepted the invitation to the game, which
eventually lead the Pandavas to their defeat
4.
5. Superplayers
• Krishna and Shakuni can be considered the ‘superplayer(s)’ of this
game. i.e. player who plays other players, in the sense that all the
events leading to the war were operated by them . It was Krishna who
constantly advised Pandavas on what to do next and Shakuni who
extracts his revenge on the Kuru clan by manipulating Duryodhana.
6. • The asymmetry of information that leads to decisive one sided
outcomes in different rounds.
• The decision of the Pandavas to play the gamble, the decision of
Kauravas to go to war, the decision to enter the Chakravyuha and
even the killing of Karna by Pandavas are all examples of asymmetry
of information at play. It makes great sense to reiterate the words of
William Shakespeare:
• “To be or not to be is the question.”
7.
8. Symmetric vs. Asymmetric
• One of the simplest classifications of games is based on their
symmetry. A symmetric game describes an environment in which
each player has the same goals and the results will only depend on
the strategies involved. Chess is a classic example of a symmetric
game. Many of the situations we encountered in the real world lack
the mathematical elegance of symmetry as participants often have
different and even conflicting goals.
• A business negotiation is an example of asymmetric game in which
each party has different goals and evaluates the results from a
different perspective (ex: winning a contract vs. minimizing an
investment).
10. Perfect vs Imperfect Information
• A perfect information game refers to an environment in which each
player can see the other player’s moves. Chess, again, is an example
of a perfect information game.
• Many modern interactions are based on environments in which the
moves from each player are hidden from other players and game
theory classifies those scenarios as imperfect information games.
• Card games like poker to self-driving car scenarios, imperfect
information games are all around us.
14. Cooperative vs. Non-Cooperative
• A cooperative game environment is one in which the different
participants can establish alliances in order to maximize the result.
• Contractual negotiations are often modeled as cooperative games.
• Non-cooperative scenarios describe environments in which players
are forbidden from forming alliances. Wars are the ultimate example
of non-cooperative games
15.
16.
17. Simultaneous vs. Sequential
• A sequential game takes place in an environment in which each player
has information about the other player earlier actions. Board games
are mostly sequential in nature.
• Simultaneous games represent scenarios in which both players can
take concurrent actions.
18. Zero-Sum vs. Non-Zero-Sum
• A zero-sum game refers to a scenario in which the gains or one player
always translate into looses for other players. Board games are
examples of zero-sum games.
• Non-zero-sum games are often encountered in scenarios in which
multiple players can benefit from the actions of one players.
• Economic interactions in which multiple participants collaborate to
increase the size of the market is an example of a non-zero-sum
game.
19. Dictator Game
• The dictator game is an experimental paradigm in which one
participant (the dictator) receives an endowment and then decides to
what extent she/he wants to split this endowment with another,
anonymous participant (the recipient).
• Standard economic theory assumes that all individuals act solely out
of self-interest. Under this assumption, the predicted result of the
dictator game is that the “dictator should keep 100% of the cake and
give nothing to the other player.” This effectively assigns the value of
what the dictator shares with the second player to zero.
20. Cornelian Dilemma
• A Cornelian dilemma is a dilemma in which someone is obliged to
choose one option from a range of options all of which reveals a
detrimental effect on themselves or someone near them.
• In classical drama, it will typically involve the character experiencing
an inner conflict, forcing them to choose between love and honor or
inclination and duty.
21.
22. Metagame
• A metagame, known as a hypergame, occurs when one player does not
know or fully understand all the strategies of a game.
• Hypergame theory extends the advantages of game theory by allowing a
player to outmaneuver an opponent and obtaining a more preferred
outcome with a higher utility.
• The ability to outmaneuver an opponent occurs in the hypergame because
the different views (perception or deception) of opponents are captured in
the model, through the incorporation of information unknown to other
players (misperception or intentional deception).
• The hypergame model more accurately provides solutions for complex
theoretic modeling of conflicts than those modeled by game theory and
excels where perception or information differences exist between players
23. • Decision theory is a formal mathematical theory about how decision-makers
make rational decisions. It is also known as normative decision theory, Bayesian
decision theory, rational choice theory, and statistical decision theory . Decision
theory predates the development of game theory and can be divided into three
parts: normative, descriptive, and prescriptive .
• Normative decision theory studies the ideal agent and the decisions that this
perfectly rational agent would make, often referred to as the study of how
decisions should be made.
• Descriptive decision theory studies the nonideal agent, such as humans, and how
they make decisions, often referred to the study of how decisions are made in
reality.
• Prescriptive decision theory studies how nonideal agents, given their
imperfections, can improve the decisions.
24. Bounded Rationality
• Bounded rationality is where a player’s rationality is limited in the
decision-making process by the information the player has, cognitive
limitations of their minds, and time available to make the decision.
• It was Hrbert Simon who originally proposed the concept of bounded
rationality as an improvement to the model of human decision-
making. Bounded rationality helps to explain why the most rational
decision is not always the decision chosen by the player in game
theory or decision theory.
25. • Bounded rationality does not mean irrationality, since players want to
make rational decisions, but cannot always do so . Players are often
very complex, but in order to be fully rational they need unlimited
cognitive capabilities .
• The cognitive capabilities of players are limited and therefore cannot
conform to full rationality. Players will use the cognitive resources
they have, with the information available, and often within time
constraints to reach a decision that is as rational as possible.
• Bounded rationality allows the player to make a decision based on
their perceived state of the game or environment, leading to multiple
players having different perceptions of the game or interaction.
27. Centipede Game
• As an example, consider the following version of the centipede game
involving two players, Jack and Jill. The game starts with a total $2 payoff.
Jack goes first, and has to decide if he should "take" the payoff or "pass." If
he takes, then he gets $2 and Jill gets $0, but if he passes, the decision to
“take or pass” now must be made by Jill.
• The payoff is now increased by $2 to $4; if Jill takes, she gets $3 and Jack
gets $1, but if she passes, Jack gets to decide whether to take or pass. If
she passes, the payoff is increased by $2 to $6; if Jack takes, he would get
$4, and Jill would get $2. If he passes and Jill takes, the payoff increases by
$2 to $8, and Jack would get $3 while Jill got $5.
• The game continues in this vein for a total of 100 rounds. If both players
always choose to pass, they each receive a payoff of $50 at the end of the
game. Note that the money is contributed by a third party and not by
either player.
28. Ultimatum Game
• The ultimatum game is an experimental economics game in which
two parties interact anonymously and only once, so reciprocation is
not an issue. The first player proposes how to divide a sum of money
with the second party. If the second player rejects this division,
neither gets anything.
29.
30.
31. • Iterated Games - When players interact by playing a similar stage
game (such as the prisoner's dilemma) numerous times, the game is
called an iterated (or repeated) game. Unlike a game played once, a
repeated game allows for a strategy to be contingent on past moves,
thus allowing for reputation effects and retribution.
• Non Iterated Games -
34. Deterministic Game
• A game is deterministic if the resolution of player actions leads to
completely predictable outcomes. It is indeterministic to one degree
or another if actions lead to potentially chaotic outcomes. ... A sense
of indeterminism, or luck, often makes a game exciting.
35. Stochastic Game
• Stochastic Games - In game theory, a stochastic game, introduced by Lloyd
Shapley in the early 1950s, is a repeated game with probabilistic transitions
played by one or more players. The game is played in a sequence of stages.
At the beginning of each stage the game is in some state.
• The players select actions and each player receives a payoff that depends
on the current state and the chosen actions. The game then moves to a
new random state whose distribution depends on the previous state and
the actions chosen by the players.
• The procedure is repeated at the new state and play continues for a finite
or infinite number of stages. The total payoff to a player is often taken to
be the discounted sum of the stage payoffs or the limit inferior of the
averages of the stage payoffs.
36. Strategies
• For agent i, a deterministic strategy specifies a choice of action for i
• at every stage of every possible history A mixed strategy is a probability
distribution over deterministic strategies Several restricted classes of
strategies:
As in extensive-form games, a behavioral strategy is a mixed strategy in
which the mixing take place at each history independently.
A Markov strategy is a behavioral strategy such that for each time t, the
distribution over actions depends only on the current state But the
distribution may be different at time t than at time t' ≠ t
A stationary strategy is a Markov strategy in which the distribution over
actions depends only on the current state (not on the time t)
39. Bertrand Model
• Bertrand competition is a model of competition used in economics, named
after Joseph Louis François Bertrand (1822–1900). It describes interactions
among firms (sellers) that set prices and their customers (buyers) that
choose quantities at the prices set. The model was formulated in 1883 by
Bertrand
• The model rests on very specific assumptions. There are at least two firms
producing a homogeneous (undifferentiated) product and cannot
cooperate in any way. Firms compete by setting prices simultaneously and
consumers want to buy everything from a firm with a lower price (since the
product is homogeneous and there are no consumer search costs). If two
firms charge the same price, consumers' demand is split evenly between
them. It is simplest to concentrate on the case of duopoly where there are
just two firms, although the results hold for any number of firms greater
than one.
40. • Crucial assumption about the technology is that both firms have the same
constant unit cost of production, so that marginal and average costs are
the same and equal to the competitive price. This means that as long as
the price it sets is above unit cost, the firm is willing to supply any amount
that is demanded (it earns profit on each unit sold).
• If price is equal to unit cost, then it is indifferent to how much it sells, since
it earns no profit. Obviously, the firm will never want to set a price below
unit cost, but if it did it would not want to sell anything since it would lose
money on each unit sold. In summary, Bertrand competition is often
characterized as harsh, cutthroat competition between firms, driving prices
down to marginal cost through a series of price undercutting.
41. • The Stackelberg leadership model is a strategic game in economics in
which the leader firm moves first and then the follower firms move
sequentially. It is named after the German economist Heinrich
Freiherr von Stackelberg who published Market Structure and
Equilibrium (Marktform und Gleichgewicht) in 1934 which described
the model.
• In game theory terms, the players of this game are a leader and a
follower and they compete on quantity. The Stackelberg leader is
sometimes referred to as the Market Leader.
42. • Firms may engage in Stackelberg competition if one has some sort of
advantage enabling it to move first. More generally, the leader must
have commitment power. Moving observably first is the most obvious
means of commitment: once the leader has made its move, it cannot
undo it - it is committed to that action. Moving first may be possible if
the leader was the incumbent monopoly of the industry and the
follower is a new entrant. Holding excess capacity is another means of
commitment.
43. • Stackelberg model remains an important strategic model in
economics. This model is useful to a firm when it realizes prospects of
profitability under the first-mover advantage concept.
• A practical instance where commitment to the first move is shown by
leaders is capacity expansion. It is assumed that the action can not be
undone. In principle, Stackelberg strategy is important where the first
mover, the leader, acts irrespective of what the action of the follower
is going to be.
44. • Cournot competition is an economic model describing an industry
structure in which rival companies offering an identical product
compete on the amount of output they produce, independently and
at the same time. It is named after its founder, French mathematician
Augustin Cournot.
45. Key Takeways
• Cournot competition is an economic model in which competing firms
choose a quantity to produce independently and simultaneously.
• The model applies when firms produce identical or standardized
goods and it is assumed they cannot collude or form a cartel.
• The idea that one firm reacts to what it believes a rival will produce
forms part of the perfect competition theory
