prisons-dilemma.Rmd

Single-round, multiple person Prisoner's Dilemma. 
I want to maximize my payout. 


If I choose `c` and everyone else choses `d` then I get `0`.


```{r}
library(tidyverse)
```


```{r}
p1_payout <- function(p1, p2) {
  case_when(
    p1 == 'c' & p2 == 'c' ~ 3,
    p1 == 'c' & p2 == 'd' ~ 0,
    p1 == 'd' & p2 == 'c' ~ 5,
    p1 == 'd' & p2 == 'd' ~ 1
  )
}
```


```{r}
p1_payout('d', 'd')
p1_payout('d', c('d', 'd'))
```

```{r}
opponent_choices <- tibble(cs = 0:19) %>%
  rowwise() %>%
  mutate(choices = list(c(rep('c', cs), rep('d', 19 - cs))))

head(opponent_choices)
```

```{r}
p1_outcomes <- opponent_choices %>%
  ungroup() %>%
  full_join(tibble(p1 = c('c', 'd')), by = character()) %>%
  rowwise() %>%
  mutate(payoff = sum(p1_payout(p1, choices)))

p1_outcomes
```

```{r}
p1_outcomes %>%
  select(-choices) %>%
  pivot_wider(names_from = p1, values_from = payoff)
```


```{r}
p1_outcomes %>%
  ggplot() + 
  geom_line(aes(cs, payoff, color = p1))
```