Rules, Games, and Common-Pool Resources

by Elinor Ostrom, Roy Gardner, James Walker

Explores ways that the tragedy of the commons can be avoided by people who use common-property resources

Genres: Economics

385 pages, Paperback

First published May 15, 1994

About the author

Elinor Ostrom won the 2009 Nobel Prize in Economics.

Reviews

[Thomas Ray]

Rules, Games, & Common-Pool Resources, Elinor Ostrom, Roy Gardner, and James Walker, 1994, 369 pages, Library-of-Congress HB 846.5 O85 1994, ISBN 0472095463. Chapters 10-13 by Shui Yan Tang (irrigation), Edella Schlager (inshore fishing), Arun Agrawal (Indian forests), William Blomquist (Southern California groundwater).

Seeks to know how resources should be allocated for /economic efficiency/ (maximize discounted net present value) and /Pareto optimality/ (no one can be made better off without making someone worse off). p. 9.

The /efficient level/ of appropriation is where marginal cost of appropriation equals marginal return. pp. 9-10.

Ostrom et al. explain the following very clearly, but it does take concentration to follow:

NONCOOPERATIVE GAME THEORY

These simple thought experiments help illuminate real situations.


Prisoner's Dilemma and similar: 2 players, each with a single, binary, choice: 4 possible outcomes. Any pair of strategies (choices) such that each player maximizes his or her payoff given what the other player does, is called a /Nash equilibrium/. Being a Nash equilibrium is a necessary condition for a pair of strategies to be a solution to a game. Every finite game must have at least one Nash equilibrium. p. 54.

If both players choose "strategy 1," each gets outcome "a."
If both players choose "strategy 2," each gets outcome "d."
If they differ, the player choosing "strategy 1" gets outcome "b;" the player choosing "strategy 2" gets outcome "c."

If c > a, a player chooses strategy 2 if he thinks the opponent will choose strategy 1.
If d > b, a player chooses strategy 2 if he thinks the opponent will choose strategy 2.
If c > a AND d > b, both players choose strategy 2.
This is the Prisoner's Dilemma:
Strategy 1 is keep quiet.
Strategy 2 is confess.
a is 1 year in jail on a lesser charge.
b is 10 years in prison, ratted out by your partner.
c is 3 months in jail, for cooperating.
d is 8 years in prison, having confessed.
Confess, for both prisoners, is the only Nash equilibrium in this game.

Notice we're only ever comparing a with c, and b with d.

However, what makes the Prisoner's Dilemma a dilemma is that
a > d.
The "dominant" strategy and Nash equilibrium, both prisoners confess, is "Pareto inferior," in that both would be better off if both had kept quiet. p. 56.

The Prisoner's Dilemma was invented as a counterexample to the "Invisible Hand" doctrine that "there is no conflict between individual and group rationality." p. 56.

The moral is, don't be a prisoner. Ostrom indeed finds that where users of common-pool resources can cooperate to set rules they can abide by, the resource can be managed for everyone's continuing benefit.

The other possibilities:

If a > c, a player chooses strategy 1 if he thinks the opponent will choose strategy 1.
If b > d, a player chooses strategy 1 if he thinks the opponent will choose strategy 2.
If a > c AND b > d, both players choose strategy 1.
Strategy 1 is the only Nash equilibrium. ("Symmetric equilibrium," both choose same strategy, p. 55.)

If a > c, a player chooses strategy 1 if he thinks the opponent will choose strategy 1.
If d > b, a player chooses strategy 2 if he thinks the opponent will choose strategy 2.
If a > c AND d > b, each player chooses the strategy he expects the opponent to choose.
The two Nash equilibria are: strategy 1 for both players, and, strategy 2 for both players. ("symmetric equilibrium," p. 55.)

Where a > c AND d > b AND a > d, the game is Assurance. p. 56. We each want to choose strategy 1 UNLESS the opponent chooses strategy 2.

If c > a, a player chooses strategy 2 if he thinks the opponent will choose strategy 1.
If b > d, a player chooses strategy 1 if he thinks the opponent will choose strategy 2.
If c > a AND b > d, each player chooses the strategy he expects the opponent NOT to choose.
The two Nash equilibria are, player 1 strategy 1, player 2 strategy 2, and, player 1 strategy 2, player 2 strategy 1. ("asymmetric equilibrium," p. 55.)

Where c > a AND b > d AND a > d, the game is Chicken. p. 56. We each want to choose strategy 1 UNLESS the opponent chooses strategy 1.
Strategy 1: drive into the ditch.
Strategy 2: stay on the road.
a = wreck your car.
b = wreck your car and get called a chicken.
c = save your car and call your opponent a chicken.
d = die.

This is one of those games it's wiser not to play.

NONCOOPERATIVE COMMON-POOL-RESOURCE GAMES:

APPROPRIATION EXTERNALITY pp. 56-58

Two players, two strategies:
Strategy 1: invest in common-pool resource.
Strategy 2: work for wages elsewhere.
a: half of what the two of you extract
b: all of what you alone extract
c: your wage
d: your wage.
b > d: Choose strategy 1 if opponent chooses strategy 2.
b > a. This is the externality.
If c > a, then our equilibria are asymmetric: each wants to do what the other does not do: a form of Chicken.
If a > c, then strategy 1 for both players is the equilibrium.
But if b + c > 2a, then the two players together do worse, following their dominant strategy, than they could have done by cooperating to choose opposite strategies. This is a form of Prisoner's Dilemma. p. 58.

ASSIGNMENT GAMES

Fishing spot 1 is better (value v1) than fishing spot 2 (value v2).
Strategy 1: fish spot 1.
Strategy 2: fish spot 2.
a = v1/2
b = v1
c = v2
d = v2/2

If v1 > 2*v2, then a > c and b > d; the one equilibrium is, both fishers use spot 1.
But b + c > 2a: Together on spot 1, they net only v1. Had they split, they would together have netted v1 + v2. Together they do worse following their dominant strategy than they could have by cooperating to fish different spots. A prisoner's-dilemma-like result.

Or if v1 = 2*v2: a = c, b > d.
If the opponent fishes spot 2, I want to fish spot 1.
If the opponent fishes spot 1, I'll be equally rewarded by fishing either spot.
Here there are 3 equilibria: two to split up (which maximizes total catch for the two fishers), one to share spot 1 (a lower-total-catch dilemma).

Or if v1 < 2*v2: c > a, b > d. We each want to do what the other does not do--but we each hope to fish spot 1. Neither of us wants to get less than the other, for the same effort. We may both choose spot 1, though spot 2 would have netted more than our half of spot 1's catch. This is a form of Chicken. p. 60.

MIXED (PROBABILISTIC) STRATEGY EQUILIBRIUM pp. 60-61

Suppose v1 = 8, v2 = 6.
Neither knows what the other will do.
Suppose each fisher has probability P of going to spot 1, probability (1 - P) of choosing spot 2.

The expected payoff of going to spot 1 is:
P * (v1)/2 + (1 - P)*(v1) = (v1)(1 - P/2)

= P * 8/2 (when someone is already there)
+
(1 - P)*8 (the other fisher has gone to spot 2.)
= 8 - 4P

The expected payoff of going to spot 2 is:
(1 - P) * (v2/2) + P*v2 = (v2/2)(1 + P)

= (1 - P) * 6/2 (when someone is already there)
+
P*6 (the other fisher has gone to spot 1.)
= 3 + 3P

If the payoff, 8 - 4P, from choosing spot 1 were higher than that for spot 2, 3 + 3P, then we would increase P. And conversely. So we maximize our payoff, in this noncooperative game, by setting
(v1)(1 - P/2) = (v2/2)(1 + P)
v1 - v1*P/2 = v2/2 + P*v2/2
v1 - v2/2 = (v1/2 + v2/2)P
P = (2*v1 - v2)/(v1 + v2)

8 - 4P = 3 + 3P
P = 5/7

The expected value of either spot is
3*v1*v2/(2(v1 + v2) )
= 144/28 = 36/7 = 5 + 1/7,
which is less than the worst individual fishing spot's value. Pareto inferior. Noncooperative games are often inferior.

RESOURCE PROVISION pp. 61-62

Two players.
Strategy 1: contribute to the provision of the resource.
Strategy 2: don't contribute; work for wages elsewhere.
For each contribution by anyone, each player gets v.
A noncontributor also receives wages w.
a: 2 v
b: v
c: v + w
d: w
If v > w, then a > c and b > d: both choose strategy 1.
If v = w, then a = c and b = d: If /I/ contribute, then the /other/ player gets more than he would have if I hadn't contributed--but, /I/ get the same amount whether I contribute or not. All 4 possible outcomes are Nash equilibria. But a contributor will be angry that his noncontributor opponent got more than the contributor got.
If w > v, then c > a and d > b: both players choose strategy 2, the only Nash equilibrium. But if 2v > w, it's Pareto inferior: they'd both be better off had both contributed. This is a kind of Prisoner's Dilemma.

The above is the easy stuff. Then come cases of varying costs and benefits of, say, monitoring for cheating by opponents.



The later chapters, that summarize research on irrigation, fishing, forests, and groundwater, are not as illuminating as the individual case studies presented in Ostrom's earlier /Governing the Commons/.

[Toni Marcheva]

Excellent, easily understandable book about economics' contribution to the study of common pool resource dilemmas.

[Brolaref]

Banger

[Richard]

(Referred to in Jared Diamond's Collapse: How Societies Choose to Fail or Succeed.)