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---
title: "Why Are There Wars?"
subtitle: POSC 1020 -- Introduction to International Relations
author: Steven V. Miller
institute: Department of Political Science
titlegraphic: /Dropbox/teaching/clemson-academic.png
date:
fontsize: 10pt
output:
beamer_presentation:
template: ~/Dropbox/miscelanea/svm-r-markdown-templates/svm-latex-beamer.tex
latex_engine: xelatex
dev: cairo_pdf
fig_caption: false
slide_level: 3
make149: true
mainfont: "Open Sans"
titlefont: "Titillium Web"
---
```{r setup, include=FALSE, cache=F, message=F, warning=F, results="hide"}
knitr::opts_chunk$set(cache=TRUE, warning=F)
knitr::opts_chunk$set(fig.path='figs/')
knitr::opts_chunk$set(cache.path='cache/')
knitr::opts_chunk$set(
fig.process = function(x) {
x2 = sub('-\\d+([.][a-z]+)$', '\\1', x)
if (file.rename(x, x2)) x2 else x
}
)
```
```{r loadstuff, include=FALSE}
# knitr::opts_chunk$set(cache=FALSE)
library(tidyverse)
library(stevemisc)
library(maddison)
library(DiagrammeR)
InterWars <- read_csv("~/Dropbox/data/cow/wars/Inter-StateWarData_v4.0.csv")
ExtraWars <- read_csv("~/Dropbox/data/cow/wars/Extra-StateWarData_v4.0.csv")
IntraWars <- read_csv("~/Dropbox/data/cow/wars/Intra-StateWarData_v4.1.csv")
DDY <- read_csv("~/Dropbox/projects/mid-project/gml-mid-data/2.02/gml-ddy-disputes-2.02.csv")
States <- read_csv("~/Dropbox/data/cow/states/states2016.csv")
States %>%
mutate(endyear = ifelse(endyear == 2011, 2015, endyear)) %>%
rowwise() %>%
mutate(year = list(seq(styear, endyear))) %>%
ungroup() %>%
unnest() %>%
arrange(ccode, year) %>%
select(ccode, year) %>%
distinct(ccode, year) -> CYs
```
# Introduction
### Puzzle(s) for Today
*War is a costly and ultimately inefficient means to address disputes. So why does it happen?*
### War is Fortunately Still a Rare Event
We care about war because of its costs, but most countries are at peace most of the time.
### The American Case
Consider the case of the United States and American deaths from:
- 9/11: 2,996
- Terrorism: around a dozen per year (recent spikes in Orlando, San Bernardino)
- Iraq War: 4,493
- Murder, average year: 16,121
- Car accidents, average year: 33,804
- Accidental falls, average year: 30,208
- Diabetes as underlying condition, 2015: 79,535
###
```{r perc-states-war-by-year-1816-2010, eval=T, echo=F, fig.height=8.5, fig.width=14, message = F}
CYs %>%
group_by(year) %>%
summarize(numstates = n()) -> Numstates
DDY %>%
filter(hostlev == 5) %>%
distinct(ccode1, year, .keep_all=TRUE) %>%
group_by(year) %>%
summarize(numstateswars = n()) %>%
left_join(Numstates, .) %>%
mutate(numstateswars = ifelse(is.na(numstateswars), 0, numstateswars),
perc = mround2(numstateswars/numstates)) %>%
ggplot(.,aes(year, perc)) + theme_steve_web() +
geom_bar(stat="identity", fill="#f8766d", alpha=0.8, color="black") +
xlab("Year") + ylab("Percentage of the State System") +
scale_x_continuous(breaks = seq(1820, 2010, by = 10)) +
labs(title = "The Percentage of States Involved in Interstate War by Year, 1816-2010",
subtitle = "We treat interstate war as (fortunately) a rare event but the 1860s, 1910s, and 1940s stand out as particularly violent decades.",
caption = "Data: GML MID data (v. 2.02) and Correlates of War State System Membership List.")
```
<!-- ![Percentage of States Involved in Interstate War (Figure 3.1)](figure31.png) -->
### Defining our Terms
Let's be clear with our terms:
- *War*: Sustained combats between at least two participants that meets a miminum severity threshold.
- Practically: 1,000 battle-related deaths per year (excluding civilian casualties).
- *Interstate*: a subset of war between at least two state system members.
- *State*: commonly a country, but with some caveats
- e.g. recognition, population size
# What Do States Fight Over?
### Kashmir: Breathtaking, but Strategically Not That Valuable
![Kashmir is breathtaking but ultimately strategically worthless](kashmir.jpg)
### Territorial Claims in Kashmir
![Territorial Claims in Kashmir](kashmir-dispute.jpeg)
<!-- ### The Importance of Territory
![The Distribution of Wars by Issue (Vasquez, 1993 via Holsti, 1991)](tab1.png) -->
###
```{r wars-by-issue-type-holsti-vasquez, eval=T, echo=F, fig.height=8.5, fig.width=14, message = F}
tribble(
~period, ~Type, ~perc, ~count,
#-----, -------, -----, -----
"1648-1714", "Territory", 77, 17,
"1648-1714", "Territory + Territory-related", 86, 19,
"1648-1714", "Other Issue", 14, 3,
"1715-1814", "Territory", 72, 26,
"1715-1814", "Territory + Territory-related", 83, 4+26,
"1715-1814", "Other Issue", 17, 6,
"1815-1914", "Territory", 58, 18,
"1815-1914", "Territory + Territory-related", 84, 18+8,
"1815-1914", "Other Issue", 16, 5,
"1918-1941", "Territory", 73, 22,
"1918-1941", "Territory + Territory-related", 93, 28,
"1918-1941", "Other Issue", 7, 2,
"1945-[1990]", "Territory", 47, 27,
"1945-[1990]", "Territory + Territory-related", 79, 27+19,
"1945-[1990]", "Other Issue", 21, 12
) %>%
mutate(Type = forcats::fct_relevel(Type, "Territory", "Territory + Territory-related", "Other Issue"),
perc = perc/100) %>%
ggplot(.,aes(x=period, y=perc, fill=Type)) + theme_steve_web() +
geom_bar(stat="identity", position = "dodge",
alpha = I(0.8), color="black") +
xlab("Historical Period") + ylab("Percentage of All Wars") +
scale_y_continuous(labels = scales::percent) +
labs(title = "Percentage and Frequency of Wars By Issue Type, 1648-1990",
subtitle = "Most wars over time have been fought over territory or territory-related issues than other issue types.",
caption = "Data: Vasquez (1993) via Holsti (1991). Note: counts appear on top of the bars by issue-type.") +
geom_text(aes(label = count, group = Type), color="black",
position = position_dodge(width=.9), size=4,
vjust = -.5, family ="Open Sans")
```
### Wars Over Other Issues
Other issues, by contrast, are not as war-prone but can still lead to war.
- Composition of another side's regime (Iraq War, Vietnam War)
- Trade (e.g. Anglo-Dutch War)
- Various other policy concerns
- Treatment of co-ethnics has come up recently (hello, Russia...)
# Bargaining and War
### War as Failed Bargain
However, it's not as simple as saying "states fight wars over stuff." *Wars are failed bargains.*
- States have numerous issues among them they try to resolve.
- They may use threats of force to influence bargaining.
- If bargaining fails, states, per our conceptual thinking, resort to war.
### A Simple Model of Crisis Bargaining
To that end, we devise a simple theoretical model of crisis bargaining.
- There are two players (A and B).
- A makes an offer (0 $< x <$ 1) that B accepts or rejects.
- If B accepts, A gets $1 - x$ and B gets $x$.
- If B rejects, A and B fight a war.
### A Simple Model of Crisis Bargaining
The war's outcome is determined by Nature (*N*)
- In game theory, Nature is a preference-less robotic actor that assigns outcomes based on probability.
- If (A or B) wins, (A or B) gets all the good in question minus the cost of fighting a war ($1 - k$)
- Assume: $k > 0$
- Costs could obviously be asymmetrical (e.g. $k_A$, $k_B$), but it won't change much about this illustration.
- The loser gets none of the good and eats the war cost too ($-k$).
We assume minimal offers that equal the utility of war induce a pre-war bargain.
### A Simple Model of Crisis Bargaining
Here's a simple visual representation of what we're talking about.
![](crisis-bargaining.png)
```{r diagrammer-example, eval=F, echo=F, fig.height=8.5, fig.width=14, message = F}
# One of these days I'll make this work to PDF.
grViz("
digraph {
# Multiple level nodes
node [shape = square, color=CornflowerBlue]
A [label = 'A'];
0 [label = '0', shape = none];
B [label = 'B'];
1 [label = '1', shape = none];
Accept [label = '1 - x, x', shape = none];
N;
Awins [shape = none, label = '1 - k, k'];
Bwins [shape = none, label = '-k, 1 - k']
# Connect nodes with edges and labels
A -> 0
A -> B
A -> 1
B -> Accept [headlabel = 'Accept', labeldistance = 5, labelangle=75]
B -> N [label = ' Reject']
N -> Awins [headlabel = 'A wins (1 - p)', labeldistance=4.5 ,
labelangle=75]
N -> Bwins [label = 'B wins (p)']
}
[1]: 'A'
[2]: '0'
[3]: paste0('Model 3\\n Split 3')
[4]: paste0('Model 6\\n Split 4')
")
# rsvg::rsvg_png(full_game, "full-game.pdf")
svgd <- export_svg(full_game)
export_graph(svgd)
pdf_digraph <- function(filename, code){
capture.output({
g <- grViz(paste("digraph{", code, "}"))
DiagrammeRsvg::export_svg(g) %>% charToRaw %>% rsvg::rsvg_pdf(filename)
}, file='NUL')
knitr::include_graphics(filename)
}
# cat(export_svg(grViz("digraph {A -> B}")), file='ouput.svg')
pdf_digraph(full_game, "node [shape = square, color=CornflowerBlue]
A [label = 'A'];
0 [label = '0', shape = none];
B [label = 'B'];
1 [label = '1', shape = none];
Accept [label = '1 - x, x', shape = none];
N;
Awins [shape = none, label = '1 - k, k'];
Bwins [shape = none, label = '-k, 1 - k']
# Connect nodes with edges and labels
A -> 0
A -> B
A -> 1
B -> Accept [headlabel = 'Accept', labeldistance = 5, labelangle=75]
B -> N [label = ' Reject']
N -> Awins [headlabel = 'A wins (1 - p)', labeldistance=4.5 ,
labelangle=75]
N -> Bwins [label = 'B wins (p)']")
```
### Solving This Game
How do we solve this game? How do A and B avoid a war they do not want to fight?
- The way to solve extensive form (i.e. "tree") games like this is **backwards induction**.
- Players play games ex ante (calculating payoffs from the beginning)
rather than ex post (i.e. hindsight).
- They must anticipate what their choices to begin games might do as
the game unfolds.
In short, we can solve a game by starting at the end and working
back to the beginning.
### Solving This Game
For our purpose, we need to get rid of Nature.
- Nature doesn't have preferences and doesn't "move." It just assigns outcomes.
- Here, it simulates what would happen if B rejected A's demand.
We can calculate what would happen if Nature moved by calculating the expected utility of war for A and B.
### Expected Utility for A of the War
\begin{eqnarray}
EU(\textrm{A} | \textrm{B Rejects Demand)} &=& (1 - p)(1 - k) + p(-k) \nonumber \\
&=& 1 - k - p + pk - pk \nonumber \\
&=& 1 - p - k \nonumber
\end{eqnarray}
### Expected Utility for B of the War
\begin{eqnarray}
EU(\textrm{B} | \textrm{B Rejects Demand)} &=& (1 - p)(-k) + p(1 - k) \nonumber \\
&=& -k + pk + p - pk \nonumber \\
&=& p - k \nonumber
\end{eqnarray}
### The Game Tree, with Nature Removed
![](crisis-bargaining-no-nature.png)
### Solving This Game
Now, continuing the backward induction, we focus on B.
- B ends the game with the decision to accept or reject.
- B does not need to look ahead, per se. It's now evaluating whether it maximizes its utility by accepting or rejecting a deal.
### Solving This Game
Formally, B rejects when $p - k > x$.
- It accepts when $x \ge p - k$.
- Notice A has a "first-mover advantage" in this game.
- This allows it to offer the bare minimum to induce B to accept.
- It would not offer anymore than necessary because that drives down A's utility.
We say A's offer of $x = p - k$ is a minimal one for B to accept.
### Solving This Game
Would A actually offer that, though?
- In other words, are $x = p - k$ and $1 - x \ge 1 - p - k$ both true?
Recall: we just demonstrated $x = p + k$. From that, we can say $1 - x \ge 1 - p - k$ by definition.
- The costs of war ($k$) are positive values to subtract from the utility of fighting a war.
### The Proof
What A would get (1 - *x*) must at least equal 1 - *k - p*. Therefore:
\begin{eqnarray}
1 - x &\ge& 1 - k - p \nonumber \\
1 - 1 + k + p &\ge& x \nonumber \\
p + k &\ge& x \nonumber
\end{eqnarray}
### Solving This Game
We have just identified an equilibrium where two states agree to a pre-war solution over a contentious issue.
- There exists a bargaining space where A and B resolve their differences and avoid war.
###
![The Bargaining Space](bargaining-space.png)
## War as an Ultimatum Game
### War as an Ultimatum Game
If you know some game theory, this looks like an ultimatum game. It is.
### War as an Ultimatum Game
Assume you and I cannot agree how to split $100.
- I want all of it. So do you.
- For $20, we can set up a fight for $100.
- First one to say "matté" (i.e. tap out, a la *Bloodsport*) loses.
- Assume *p* = .5, our EU(fighting) = (100)(.5) + (0)(.5) - 20 = 30
### Would You 'Kumite' for $100 in This Situation?
![](bloodsport.jpg)
### Yes, You Would...
By itself, this is a fantastic lottery.
- For $20, you win $30 on average.
- We would agree to fight if this accurately represented our payoffs.
### War as an Ultimatum Game
Consider that I offer you a deal in light of this. I take $70; you take $30. Would you accept this? Assume:
- You are risk-averse and would take a deal that matches your expected utility for fighting.
- You are not permitted a counter-offer.
You might decry this as unequal. It is...
### War as an Ultimatum Game
However, you would accept this if you were rational.
- My offer to you just matched your expected utility of fighting.
- You would accept this, per our assumptions.
- Any offer I give to you between $30 and $70 would induce you to accept.
- I would not offer you $70, though, because that reduces my payout.
# Conclusion
### Conclusion
- War is the most destructive/costly thing we do.
- Fortunately, it's a rare event.
- States mostly fight over the distribution of territory.
- Conceptually: war is bargaining failure.
- We'll talk more next about why exactly bargaining fails.
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