List of games in Chapter 4 Uncertainty

Using Comlabgames

Game title

(right click on the game to download it)

Short description of the experiment

4.1. Direct Foreign Investment

The extensive form of a game in which a multinational is deliberating over the prospect of acquiring a plant in new, previously unexplored territory. Having already undertaken some study, it must choose between making a final decision now, or deferring until more information is gathered and processed. The factory's condition is determined before the firm takes its first decision, and it is not revealed until after a decision has been taken.

4.2. Product Testing

A pharmaceutical company which cannot market a drug unless it has passed guidelines set out by the Federal Drug Administration. There are two tests that must be passed before marketing is permitted.

4.3. Filling a Vacancy

4.4: Certainty Equivalence

In this experiment subjects are asked to how much they are willing to pay for a lottery called L when its probabilities are known. The number is called b for bid.

-A random number n from a probability distribution which lies between 0 and 100 is then drawn.

- If n ≤ b, then a subject pays n in exchange for the lottery L, and receives the payoff from playing the lottery.

- If b < n, then a subject neither pays nor receives anything.

4.5: Insurance

To illustrate this point suppose that a driver begins with wealth w and faces a gamble in which she might lose d from damage in the event of a accident which occurs with probability p. To offset this potential loss an insurance company offers her the opportunity to reimburse her q∈[0,d] for her loss, for a premium of qf . Suppose the driver has an expected utility maximizer with a twice differentiable, increasing utility function u(w) defined on her wealth w. How much insurance should she buy? A risk neutral driver fully insures his vehicle if the rate better than actuarially fair but buys no insurance if it is unfacorable to him. Finally a risk seeker does not buy any insurance sold at actuarilly fair rates, but can be induced to buy it at rates that are favorable to him. Suppose the driver is risk averse. If she only partially insures herself with q<d units, her expected utility is:

But we see from the top line that a utility of u(w-qf) can be obtained if insurance is actuarially fair, which means f=p per unit, and the driver prurchases full insurance, setting q=d. It follows that a risk averse driver would fully insure his vehicle if the premium is actuarially fair. However if the premium was less favorable to the driver, the discussion in the next example below demonstrates that even a risk averse driver would not fully insure his vehicle, prefering to take on some risk. In this case the risky asset, a partially uninsured vehicle, offers a higher expected return than the safe full insurance alternative.

In the following experiment, suppose u(w) =-exp(αw) and f and p=0.1.

4.6: Pension fund

Consider a worker planning retirement who allocates w, the amount of wealth to be invested for future consumption, between buying shares in a pension fund with a random return denoted by π, and saving at a constant interest rate denoted by r. Alternatively we might like to think of the proportion a pension fund allocates to bonds and the amount allocated to stocks. Denoting the amount of his wealth deposited in his savings account by s, the amount of wealth consumed in retirement is then

c=s(1+r)+(w-s)π

The worker chooses between savings and consumption

In an experiment we normalized wealth to unity, that is w=1, let the utility function take the function form u(c)=c^γ , set the interest rate r to zero and assumed π is uniformly distributed between π and π+1 for some real number π.

4.7: Portfolio choice

4.8: Allais paradox

Subjects choose between:

Choice 1:

A: $300 with a 1.0 chance or B: $400 with a 0.8 chance

Choice 2:

C: $300 with a 0.25 chance or D: $400 with a 0.2 chance

A clear majority of people choose A and D but this violates independence since C and D are 'scaled-down' versions of A and B (i.e. they are both scaled down by a factor of 0.25)

4.9: Ellsberg paradox

In the urn there are 90 balls: 30 of those balls are blue, the other 60 are either red or yellow. What is the task? Subjects will be asked to choose among assets that pay real money according to the color of the ball that will be drawn from the urn.

Choice 1: Choice between asset a) or asset b)

	Blue ball	Red ball	Yellow ball
a)	$10	$0	$0
b)	$0	$11	$0

Choice 2: Choice between asset a) or asset b)

	Blue ball	Red ball	Yellow ball
a)	$10	$0	$0
b)	$0	$0	$11

Choice 3: Choice between asset a) or asset b)

	Blue ball	Red ball	Yellow ball
a)	$10	$0	$11
b)	$0	$10	$11

4.10: First order stochastic dominance

Subjects are asked to choose between the following two lotteries:

Lottery B : [$10 with probability 0.1, $20 with probability 0.10, . . .,

$100 with probability 0.1]:

Lottery C : [$20 with probability 0.2, $30 with 0.1, $40 with probability

0.1,. . ., $100 with probability 0.1]:

4.11: Second order stochastic dominance

Subjects are asked to choose between the following two lotteries:

Lottery A : [$10 with probability 0.5 and $100 with probability 0.5]:

Lottery B : [$10 with probability 0.1, $20 with probability 0.10, . . .,

$100 with probability 0.1]: