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Question Session 07

 

Week 07 Questions:

Philosophical Issues in Behavioural Science

this is being recorded

Alex

Does pursuing the Nash equilibrium in the gangster game forces both gangsters in the least profitable option?

hawk-dove

Gangster X
stay
home		attack
Gangster Ystay
home		2
2		1
3
attack 3
1		 0
0
check they understand

mixed strategies

hawk-dove

Gangster X
stay
home		attack
Gangster Ystay
home		2
2		1
3
attack 3
1		 0
0

Strategies: each player selects stay-home with .5 probability.

Expected payoff for X:

0.5 * (X’s payoff from stay home) = 0.5 * (0.5 * 2 + 0.5 * 1)

+

0.5 * (X’s payoff from attack) = 0.5 * (0.5 * 3 + 0.5 * 0)

= 1.5

Nash equilibrium for mixed strategies

‘Nash equilibrium is defined as a list of mixed strategies, one for each player, such that the choice of each is her best choice, in the sense of yielding the highest expected payoff for her, given the mixed strategies of the others.’ (Dixit, Skeath, & Reiley, 2014, p. 216; see Osborne & Rubinstein, 1994, p. definition §32.3 for a more formal statement)
Not going to prove it, but .5,.5 is the nash equilibrium.
online calculators are fun
https://mindyourdecisions.com/GameSolver.html
https://intranet.csc.liv.ac.uk/cgi-bin/cgiwrap/rahul/input.py

hawk-dove

Gangster X
stay
home		attack
Gangster Ystay
home		2
2		1
3
attack 3
1		 0
0

Strategies: each player selects stay-home with .5 probability.

Expected payoff for X:

0.5 * (X’s payoff from stay home) = 0.5 * (0.5 * 2 + 0.5 * 1)

+

0.5 * (X’s payoff from attack) = 0.5 * (0.5 * 3 + 0.5 * 0)

= 1.5

cardinal vs ordinal preferences

hawk-dove

Gangster X
stay
home		attack
Gangster Ystay
home		2
2		1
3
attack 3
1		 0
0

the greater the benefit from attack

-> the more frequent the attacks (at Nash equilibrium)

-> the lower expected the payoff

In hawk-dove, increasing the rewards available from attacking when the other stays at home reduces the expected payoffs at the Nash equilibrium?
Changing the costs of attack is also possible. What happens if we increase for both players the cost of attack? What happens if we increase the costs for just one player (favouritism in parenting)?
[increase costs for both -> less attack, greater expected payoff]
[increase costs for one -> other plays same .5,.5 strategy; the one with increased costs of attack decreases frequency of attack; payoffs same for one with more attack costs (1.5) but increase towards 2 for the other player (with unchanged attack costs)]
No matter what you change, you can only approach (not beat) the expected payoff of (stay-home, stay-home) -> agreements can be powerful and benefit all players even the strongest
explanation

game theory explains

Both twins would do better if they never fought ...

But if they never fought, one could do even better by attacking.

The mixed strategy Nash equilibrium predicts a relation

between the frequency of attacks and the value of rewards.

assumptions of game theory are false

objections to decision theory carry over

+

many applications of game theory assume common knowledge of rationality

DId I answer Alex’ question.

Alex

Does pursuing the Nash equilibrium in the gangster game forces both gangsters in the least profitable option?

hawk-dove

Gangster X
stay
home		attack
Gangster Ystay
home		2
2		1
3
attack 3
1		 0
0

another question

Identify any one putative objection to an assumption of decision theory.

Why might this objection also lead to an objection to Dickinson’s dual process theory of action?

Does it?

First thing: three parts.

idea 1

 

1. The Objection (e.g. Ellsberg Paradox) shows that if we characterise preferences as decision theoretic constructs, few if any people actually have preferences.

2. There is no way to characterise preferences except as decision theoretic constructs.

3. Therefore there is no way to characterise goal-directed processes

actually what does follow?
[if use decision theory to charcterise goal-directed process]
ask them to say what follows
Is this a good objection?
This seems absurd, for sure. The problem is that the premises do not seem so absurd
To strengthen this we need to look at researchers who have drawn a similar conclusion and ask what their reasons are.

‘Preferring a dominated option or expressing different preferences depending on the framing of options . . . demonstrate[s] . . . the absence of stable preferences and resulting irrational decisions’

(Simonson, 2015, p. 20)

So we should be interested to know what if anything justifies Simonson in saying this. Except he doesn’t justify it, I think. But useful pointers ...
So we need more than Ellsberg or Allais Paradox?
dominance
So we need more than Ellsberg or Allais Paradox?

‘Imagine you are about tu purchase a jacket for $125 $15 and a calculator for $125 $15.

‘The calculator salesman informs you that the calculator you wish to buyis on sale for $120 $10 at the other branch of the store located 20 minutes drive away.

Would you make the trip to the other store?

(Tversky & Kahneman, 1981, p. 212)

$5 framed as different % savings
68% would drive 20 minutes in $15 vs $10 but only 29% in the other case.

another example of framing effects

(Kahneman & Tversky, 2012, p. 272)

‘Preferring a dominated option or expressing different preferences depending on the framing of options . . . demonstrate[s] . . . the absence of stable preferences and resulting irrational decisions’

(Simonson, 2015, p. 20)

idea 1

 

1. The Objection (e.g. Ellsberg Paradox) shows that if we characterise preferences as decision theoretic constructs, few if any people actually have preferences.

2. There is no way to characterise preferences except as decision theoretic constructs.

3. Therefore there is no way to characterise goal-directed processes

What if anything justifies Chater’s conclusion?

‘The problem with measuring risk preferences is not that measurement is difficult and inaccurate; it is that there are no risk preferences to measure---there is simply no answer to how, ‘deep down’, we wish to balance risk and reward.

And, while we’re at it, the same goes for the way people trade off present against future; how altruistic we are and to whom; how far we display prejudice on gender, race, and so on ...

there is no point wondering which way of asking the question [...] will tell us what people really want.

there can be no method...that can conceivably answer this question, not because our mental motives, desires and preferences are impenetrable, but because they don’t exist’

(Chater, 2018, pp. 123--4)

idea 1

 

1. The Objection (e.g. Ellsberg Paradox) shows that if we characterise preferences as decision theoretic constructs, few if any people actually have preferences.

2. There is no way to characterise preferences except as decision theoretic constructs.

3. Therefore there is no way to characterise goal-directed processes

Cannot reject the second premise. And yet the conclusion seems clearly wrong. What to do? (It’s almost like a paradox.)
We need a positive account of preferences (and beliefs) and their role in the goal-directed process.
E.g. what happens to preferences if we switch to prospect theory?

‘Expected utility theory [...] has come under serious question [...]

There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets.

Many alternative models have been proposed’

(Tversky & Kahneman, 1992, p. 297)

idea 1

 

1. The Objection (e.g. Ellsberg Paradox) shows that if we characterise preferences as decision theoretic constructs, few if any people actually have preferences.

2. There is no way to characterise preferences except as decision theoretic constructs.

3. Therefore there is no way to characterise goal-directed processes

So maybe one of the alternative models would work?

Identify any one putative objection to an assumption of decision theory.

Why might this objection also lead to an objection to Dickinson’s dual process theory of action?

Does it?

Yuo can go either way.

more questions?