YANIS VAROUFAKIS VISITING PROFESSOR AT LBJ SCHOOL OF PUBLIC AFFAIRS PROFESSOR OF ECONOMIC THEORY AT...
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Transcript of YANIS VAROUFAKIS VISITING PROFESSOR AT LBJ SCHOOL OF PUBLIC AFFAIRS PROFESSOR OF ECONOMIC THEORY AT...
YANIS VAROUFAKIS
V I S I T I N G P R O F E S S O R AT L B J S C H O O L O F P U B L I C A F FA I R S
P R O F E S S O R O F E C O N O M I C T H E O R Y AT T H E U N I V E R S I T Y O F AT H E N S
Game TheoryAn assessment of the theory that promises to unify the social sciences
GT’s five central theorems
1. All (finite) interactions among autonomous agents have a rational ‘solution’
2. All negotiations feature a uniquely rational bargaining agreement
3. Theorems 1 and 2 extend to dynamic settings
4. Theorems 1 and 2 extend to risky choices5. No rationality required!
THEOREM 1: All finite non-cooperative interactions have a rational ‘solution’ (=equilibrium)
C1 C2 C3 C4 R1 5,12 -1,11 1,20 10,10
R2 4, -1 1,1 2,0 20, -1 R3 3,2 0,4 4,3 50,1 R4 2,101 -1,92 0,101 100,100 A static game
Nash equilibrium
A set of mutually reinforcing best replies
C1 C2 C3 C4 R1 5,12 -1,11 1,20 10,10
R2 4, -1 1,1 2,0 20, -1 R3 3,2 0,4 4,3 50,1 R4 2,101 -1,92 0,91 100,100 A static game
Nash equilibrium:
• A set of mutually best replies• A set of strategies that confirm the beliefs
that motivated them
THEOREM 1: All finite non-cooperative interactions have a rational ‘solution’ (=equilibrium)
THEOREM 1: All finite non-cooperative interactions have a rational ‘solution’ (=equilibrium)
EXISTENCE THEOREMThere exists at least one such Nash equilibrium in all possible interactions as long as:
the set of strategies is boundedagents are labouring under commonly known
instrumental rationality
Three possible critiques
Normative: Rationality means more than an incapacity to resist a net individual utility gain
Predictive: Real people are not that good at calculating (bounded rationality)
Immanent Criticism: Are the theory’s claims consistent with its assumptions?
Normative critique of instrumental rationality 1: A public good interaction
Group of N anonymous personsEach is given $10Then, each is given two options
Option 1: Keep the $10 Option 2: Contribute it to a common purse
Once all N persons have chosen, the contents of the purse are doubled (by the experimenter) and shared
Social optimum: All contribute and get $20 each
Nash equilibrium: No rational agent will contribute!Martin Hollis: A scandalous conclusion
Normative critique of instrumental rationality 2: A riddle
Mary attends her mother’s funeral. There, she spots a handsome man and develops an
urge to talk to him, with a view to asking him out. However, as the funeral comes to a close, the
handsome man disappears without Mary managing to strike a conversation.
That night, Mary murders her sister.Why did she do it?
Of 173 game theory students asked, 124 answered: “To see the handsome man again.”
Of 564 non-game theory students asked, only 32 offered the same answer
Predictive critique: Bounded rationality
1.Collective irrationality: Are you a better or worse driver than average?
2. Individual irrationality: HIV test Suppose that 100000 random tests have been
conducted Suppose that, on that basis, the test for HIV proved
accurate 99% of the time Suppose also that 0.1% of the population have HIV,
on averageYou test positive. What is the probability that you
have HIV?Answer: <10%
THEOREM 2: A unique solution for the bargaining problem
Bargaining protocolRound 1A proposes division (x1,1-x1)B accepts ENDB rejects & Counter-offers (y1,1-y1); x1 > y1
Also, he selects probability of no agreement = 1-p1
Round 2A accepts ENDA rejects Counter-offers (y2,1-y2); x2 < y2
and selects probability of no agreement = 1-p2
Rounds 3,4, ad infinitum
Defining credible rejections
Suppose at round t A demands xt and offers B 1-xt A rejection by B, followed by a counterproposal of division (yt+1,1-yt+1) and a threat of conflict equal to pt is defined as credible if and only if B expects a net gain from this rejection.
In short: ptuB(1-yt+1)>uB(1-xt)
Similarly, A’s rejection of B’s offer at t+1, yt+1, in favour of some other demand, say xt+1 , is credible if and only if
pt+1uA(xt+1)>uA(yt)
Nash’s Remarkable TheoremThere exists only a single such agreement in
every conceivable bargaining situation
An equilibrium of fear (of disagreement)
Consider division/agreement ZSuppose that if A offers Z to B, B can credibly reject Z But, at the same time, A can credibly reject any such
rejection.Suppose that the same applies if B offers Z to A.Then, Z is defined as an equilibrium of fear agreement
– an EFA
The one that maximises the product of their utilities!T
Theorem 3: First two theorems extend to dynamic settings
7 $1000 bills on a table A and B take turns to collect either 1
or 2 of them at each visit The moment a player picks up 2, the
game endsSocial optimum: Each takes one at each
visit until no money is left on the tableNash’s equilibrium: First player collects
2 bills, the second does not get to play and 5 bills are lost
Theorem 4: Theorems 1,2&3 extend to risky choices
Suppose A is ‘righteous’ (or Kantian) with probability p
Does it make sense for an instrumental A to pretend to be righteous/Kantian?
Yes, says Game Theory under the condition that…
the probability of righteousness is commonly known amongst all non-righteous players
the probability of bluffing (by non-righteous players who are pretending to be righteous) is also common knowledge amongst the non-righteous
Theorem 5: Instrumental Rationality is not even necessary!
• Agency shifts from humans to… strategies (e.g. the strategy of Richard Dawkins’ ‘selfish gene’)
• Pure adaptation of strategies• Plus random mutations• The strategy that does ‘better’ displaces the rest
Two mechanisms
An adaptation mechanism (replicator dynamic) A mutation generating mechanism (testing the
evolved strategy’s stability)
Fundamental Theorem of Evolutionary Game Theory
Every evolutionary equilibrium is a Nash equilibrium
The opposite does not hold!
Theorem 5: Evolutionary Game Theory
Immanent Criticism/internal critique
1. Too many equilibria: IndeterminacyThe more realistic the settings, the more radical indeterminacy becomes
a ttack refra in a ttack -2 ,-2 2 ,0 refra in 0 ,2 1 ,1
A sim ple co nflic t ga m e
2. Unconvincing equilibria (Non-convergence even in logical time). The static case
C 1 C 2 C 3 R 1 1 ,1 100 ,0 -100 ,1
R 2 0 ,100 1 ,1 100 ,1 R 3 1 ,-100 1 ,100 1 ,1
Immanent Criticism/internal critique
A ‘trivial’ bargaining solution?When a player rejects an offer x, and threatens
conflict with probability 1-p, Nash implicitly assumes common knowledge of 1-p, the probability of conflict
Over time, this is equivalent to assuming common knowledge of the expected duration of the negotiations
The uniqueness of the solution is thus assumed – not proven.
Nash’s proof: if there is a unique solution, it is the one that maximises the product of utilities.
Immanent Criticism/internal critique
Trivial dynamic analyses? At every juncture common knowledge of subjective probability beliefs in the context of backward induction…• An epistemological minefield…• A monologue of (instrumental) Reason on
Unreason and on alternative forms of rationality so as to keep players on the ‘equilibrium path’
• Denial of human reason’s capacity to subvert itself
Immanent Criticism/internal critique
Recapping1. An impoverished notion of Reason (instrumental
rationality) unable to shoulder the explanatory burden
2. Closure demands the radical absence of a theory of motivated errors: Players are denied even their instrumental rationality for the glory of Game Theory
3. In its evolutionary guise, Game Theory presumes uncorrelated mutations
The End of Politics and History…
Immanent Criticism/internal critique
Game Theory’s Conundrum
• Models that are either over-determined or under-determined and can only be closed by sleight of hand
• Is this surprising?
• Why have so many brilliant minds proven so uncritical in their acceptance of this research program?
The Game Theorist’s Nemesis
Constantly elevating problems onto higher planes of abstraction, without solving them
Constantly introducing less and less credible axioms for the purpose of imposing an equilibrium, with little effect:
In the end, Indeterminacy always rears its ugly head…
My end-of-the-road ‘discoveries’
Game theory brings to its logical conclusion the theoretical project of explaining the world in terms of instrumental rationality
It reaps the harvest it has sownInstrumental Reason has, and can have, no
monopoly of insights on non instrumental behaviour
Errors cannot be segregated from rational attempts to subvert logic
When assuming that such segregation is possible (as GT does), theory ends up in a logical mess
The thoughts which Game Theory cannot fathom…
It overestimates our computing power and underestimates our Reason
Albert Camus: “Man as the only creature who refuses to be what he is.”
Hegel: “It is only by being acknowledged that I can be sure that I am, and of what I am.”
The Game Theorists’ strategy
Argue that Game Theory is the common language that can help unify the social sciences Construct sophisticated interactions Behind the scenes impose equilibria in order
to ‘close’ the models Destroy all sophistication in the process
Maintain academic power by putting on display either indeterminate rich analyses or determinate poor analyses – concealing that it is impossible to have both
Attempts to civilise/socialise homo economicus lead to radical indeterminacy Psychological Game Theory
When we care not only about what others will do but also about the reasons for which they will do it
2nd order beliefs infiltrate the player’s utility function
D C D 1,1 3,0 C 0,3 2,2
The Prisoner’s Dilemma
The young Game Theorist’s Tragedy
The young game theorist’s dilemma
A truly illiberal moveTo publish, one needs to ‘close’ the modelTo close the model, the sophistication must go
and intellectually indefensible hidden axioms must be introduced.
The Dilemma‘Close’ it illicitly and lose its sophistication, as
well as any prospect of telling a useful story about truly rational people
Refuse to do so and be damned…
Four conclusions
1. GT refuses to engage in the contradictions that are endogenously generated in its models
2. GT is useful in exploring the limits of any social theory - especially of audacious ones reaching for the Theory-of-Everything-Social status
3. GT’s most peculiar grand failure is the ultimate guide to the limitations of any attempt to understand human society in terms of liberal individualism
4. Behind every toxic derivative produced by Wall Street and every macroeconomic model backing the policies that led to 2008, lurks the Hubris of the game theorist’s strategy
Lastly…
To engage in such discursive battles, graduate students must be prepared for a lonely struggle against a powerful Priesthood: “Azande see as well as we that the failure of their oracle to prophesy truly calls for explanation, but so entangled are they in mystical notions that they must make use of them to account for failure. The contradiction between experience and one mystical notion is explained by reference to other mystical notions.” (Evans- Pritchard in his Witchcraft, Oracles and Magic among the Azande, 1937)
The debris of such a path…
Rational Conflict, Oxford: Blackwell Publishers, 1991
Game Theory: a critical introduction, Routledge, (with Shaun Hargreaves-Heap), 1995
Game Theory: Critical Concepts Vol. 1-5, Routledge
Game Theory: a critical text, Routledge, (with Shaun Hargreaves-Heap), 2004
Economic Indeterminacy: An encounter with the economists’ peculiar nemesis, Routledge, 2013
The elusive arithmetic of Bayes’ Rule
(99%) true +ve = 99
(100) (1%)
HIV false –ve = 1 (0.1%)
100000Tests false +ve = 999 no HIV
(99900)true -ve = 98901
Pr(HIV│you tested +ve) = 99/(99+999) < 10%!