CORE Econ Micro

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.title[
# CORE Econ Micro
]
.subtitle[
## <div class="line-block">Strategic interactions and social dilemmas</div>
]
.author[
### Guillermo Woo-Mora
]
.date[
### <div class="line-block">Paris Sciences et Lettres<br />
Autumn 2025</div>
]

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**Social interactions**: the decisions of individuals affect other people as well as themselves

(Could be cyclist and tourists in Paris...)

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The biggest social dilemma faced by humanity right now is the problem of climate change:
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# Social interactions: Game theory
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## Social interactions: Game theory

- **Social interaction**: A situation involving more than one person/party, where one’s actions affect both their own and other people’s outcomes.
- **Strategic interaction**: A social interaction where people are aware of the ways that their actions affect others.
- **Strategy**: Action(s) that people can take when engaging in a social interaction. 
- **Game**: Models or description of strategic interactions 
- **Game theory**:  a set of models of strategic interactions. Widely used in economics and elsewhere in the social sciences.

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1. **Players** – who is involved in the interaction
2. **Feasible strategies** – actions each player can take
3. **Information** – what each player knows when choosing their action
4. **Payoffs** – outcomes for every possible combination of actions

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## Example: Crop choice

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- Two farmers decide which crop to specialize
- They interact only once (**once shot game**)
- They choose simultaneously

1. **Players** – Anil and Bala
2. **Feasible strategies** – Rice or Cassava
3. **Information** – Each farmer does not know what the other chose
4. **Payoffs** – depend on market prices and quality of land

- Anil is better at producing cassava; Bala is better producing rice
- They both sell whatever crop they produce in a nearby village market
- If they bring less of one crop, the price of such crop increases

]

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<img src="imgs/figure4-1.png" width="100%" style="display: block; margin: auto;" />
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## Example: Crop choice

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- Two farmers decide which crop to specialize
- They interact only once (**once shot game**)
- They choose simultaneously

]

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<img src="imgs/figure4-2a.png" width="100%" style="display: block; margin: auto;" />
**Pay-offs matrix**
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# Best responses: Nash equilibrium
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## Best responses: Nash equilibrium

Game theory describes social interactions; it can also help to predict what will happen.

**Best response**⁠: the strategy that will lead to a player’s most preferred outcome, given the strategies that the other players select

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Begin with the row player (Anil) and ask: ‘What would be his best response if the column player (Bala) decided to play Rice?’

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If Bala chooses Rice, Anil’s best response is Cassava—that gives him 6, rather than 4. Place a dot in the bottom left-hand cell. A dot in a cell means that this is the row player’s best response.

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If Bala chooses Cassava, Anil’s best response is Rice—giving him 6, rather than 5. Place a dot in the top right-hand cell.

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If Anil chooses Rice, Bala’s best response is to choose Rice too (4 rather than 3). Circles represent the column player’s best responses. Place a circle in the upper left-hand cell.

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Lastly, if Anil chooses Cassava, Bala’s best response is Rice again (he gets 6 rather than 2). Place a circle in the lower left-hand cell.

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**Mutual best responses**: The dot and circle coincide in the lower left-hand cell. If Anil chooses Cassava and Bala chooses Rice, the players are playing best responses to each other.

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We call this pair of strategies an **equilibrium**: a situation or model outcome that is self-perpetuating: if the outcome is reached it does not change, unless an external force disturbs it. ⁠

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In game theory, a **Nash equilibrium** is a set of strategies where each player’s choice is the best response to the others — no one can get a better outcome by changing their action alone.

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# Dominant strategy equilibrium and the prisoners’ dilemma
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## Dominant strategy equilibrium and the prisoners’ dilemma

Note that, regardless of what Anil chooses, Bala is always better off choosing rice.

`$\rightarrow$` **Rice is a dominant strategy for Bala**

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Another rice–cassava game:

Find the NE. Are there dominant strategies?
--
 **Yes: Anil's dominant strategy is Casssava, while Bala's dominant strategy is Rice**

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Another rice–cassava game:

`$$\textit{Nash Equilbrium}  = (Cassava, Rice) = \textit{Dominant strategy Equilbrium}$$`

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### The prisoners’ dilemma

Imagine that Anil and Bala are now facing another problem.

Each is deciding how to deal with pest insects that destroy the crops they cultivate in their adjacent fields.

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- The first is to use an inexpensive chemical called Toxic Tide. It kills every insect for miles around.

Toxic Tide also leaks into the water supply that they both use.

- The alternative is to use integrated pest control (IPC), in which beneficial insects are introduced to the farm.

The beneficial insects eat the pest insects.
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<img src="imgs/figure4-4a.png" width="85%" style="display: block; margin: auto;" />

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### The prisoners’ dilemma

Imagine that Anil and Bala are now facing another problem.

Each is deciding how to deal with pest insects that destroy the crops they cultivate in their adjacent fields.

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- The first is to use an inexpensive chemical called Toxic Tide. It kills every insect for miles around.

Toxic Tide also leaks into the water supply that they both use.

- The alternative is to use integrated pest control (IPC), in which beneficial insects are introduced to the farm.

The beneficial insects eat the pest insects.
]

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<img src="imgs/figure4-4b.png" width="85%" style="display: block; margin: auto;" />

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### The prisoners’ dilemma

- Are there dominant strategies?
- Is there a NE?

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# Evaluating outcomes: The Pareto criterion
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## Evaluating outcomes: The Pareto criterion

What if we want to evaluate the outcome of an economic interaction (**allocation**)?
Can we say an allocation is better or worse than alternative outcomes?

**The Pareto criterion**

Allocation A is better than allocation B if **at least one party would be strictly better off with A than B, and nobody would be worse off**.

We say that A Pareto-dominates⁠ B, or that A would be a Pareto improvement⁠ over B.

When we say an allocation makes someone ‘better off’ we mean that they prefer it, which does not necessarily mean they get more money.

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### Evaluating outcomes: The Pareto criterion

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### Evaluating outcomes: The Pareto criterion

**Comparing (T, T) and (I, I)**: The allocation at (I, I) lies in the rectangle north-east of (T, T), so an outcome where both players use IPC Pareto-dominates one where both use Toxic Tide: they both prefer (I, I).

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### Evaluating outcomes: The Pareto criterion

**Comparing (T, T) and (T, I)**: If Anil uses Toxic Tide and Bala IPC, then Anil is better off but Bala is worse off than when both use Toxic Tide. The Pareto criterion cannot say which of these allocations is better.

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### Evaluating outcomes: The Pareto criterion

**No allocation Pareto-dominates (I, I)**: None of the other allocations lie to the north-east of (I, I), so it is not Pareto-dominated.

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### Evaluating outcomes: The Pareto criterion

**What can we say about (I, T) and (T, I)?**: Neither of these allocations are Pareto-dominated, but they do not dominate any other allocations either.

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### Evaluating outcomes: The Pareto criterion

An allocation that is not Pareto-dominated by any other allocation is **Pareto efficient**⁠.

(I, T), (I, I), and (T, I).

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### Evaluating outcomes: The Pareto criterion

**Caution:**

- Pareto efficiency means no one can be made better off without making someone else worse off, but **it doesn’t imply fairness or desirability**.

- There can be **many Pareto-efficient outcomes**, and **the concept doesn’t tell us which one is best**.

- A Pareto-efficient allocation may still seem **unfair or socially undesirable**.

- When evaluating outcomes, we should **consider fairness** as well as Pareto efficiency.

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# Public good games and cooperation
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## Public good games and cooperation

Many farmers in south-east Asia rely on shared irrigation facilities that require constant maintenance and new investment.

Each farmer faces the decision of how much to contribute to these activities, which benefit the entire community.

But a farmer who does not contribute will still benefit from the contribution of others.

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## Public good games and cooperation

Imagine there are four farmers who are deciding whether to contribute to an irrigation project.

For each farmer, the cost of contributing to the project is 10.

Every contribution of 10 increases the crop yield on each of the four farms by 8.

This is a strategic interaction: the action of one farmer affects the pay-offs of the others.

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## Public good games and cooperation

Now consider the decision facing Kim, one of the four farmers.

Suppose two other farmers contribute.

If she doesn’t contribute, she will receive a benefit of 8 from each of the two contributions and incur no costs herself. Her total pay-off is 16.

|                                   | Kim does not contribute | Kim does contribute |
|-----------------------------------|--------------------------|---------------------|
| Benefit from the contribution of others | 16                       |                     |
| Plus benefit from her own contribution  | +0                       |                     |
| Minus cost of her contribution          | −0                       |                     |
| **Total**                              | **$16**                  |                     |

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## Public good games and cooperation

Now consider the decision facing Kim, one of the four farmers.

Suppose two other farmers contribute.

If she contributes too, she receives an additional benefit of 8 (and so do the other three farmers). But it will cost her 10, reducing the pay-off to 14.

|                                   | Kim does not contribute | Kim does contribute |
|-----------------------------------|--------------------------|---------------------|
| Benefit from the contribution of others | 16                       | 16                  |
| Plus benefit from her own contribution  | +0                       | +8                  |
| Minus cost of her contribution          | −0                       | −10                 |
| **Total**                              | **$16**                  | **$14**             |

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## Public good games and cooperation

**Public good game**⁠: when one individual bears a cost to provide a good, everyone receives a benefit. This creates a **social dilemma**.

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## Public good games and cooperation

A case of the prisoners’ dilemma with more than two players:

Everyone would benefit if everyone cooperated, but cooperation cannot be an equilibrium because each farmer would do better by free-riding on the others.

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# Social preferences: Altruism
]

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## Social preferences: Altruism

In real-world examples and experiments, people often play the cooperative strategy in prisoners’ dilemma games. Why?

People generally do care about what happens to others.

When people have **social preferences**⁠, their utility depends not only on what they obtain for themselves, but also on things that affect the wellbeing of other people.

**Altruism** is a social preference in which an individual’s utility is increased by benefits to others.

Other social preferences are **inequality aversion** (a preference for more equal outcomes); and **spite** and **envy**—in which cases, benefits to others may reduce the individual’s utility.

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## Modelling altruistic preferences

Zoë is given some tickets for the national lottery, and one of them wins a prize of 200.

Will she decide to keep all the money for herself, or share some of it with her flatmate, Yvonne?

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## Modelling altruistic preferences

The shaded area shows the feasible ways of sharing the prize. Zoë will choose a point on the budget constraint, sharing all of the 200 between them.

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## Modelling altruistic preferences

Zoë ’s utility depends on Yvonne’s share of the prize as well as her own. She will choose the point on the feasible frontier that gives her the highest utility.

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## Modelling altruistic preferences

She achieves the highest level of utility at A, where an indifference curve just touches the feasible frontier. She keeps 140 for herself, and gives 60 to Yvonne.

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## Modelling altruistic preferences

If Zoë cared only about money for herself, her utility would be highest at point S. She would keep the whole prize and give Yvonne nothing.