Integer objects are immutable, so you cannot modify the value once they have been created. You will need to create a new Integer and replace the existing one.
Integer objects are immutable. You can't change the value of the integer held by the object itself, but you can just create a new Integer object to hold the result:
Integer start = new Integer(5);
Integer end = start + 5; // end == 10;
As Grodriguez says, Integer objects are immutable. The problem here is that you're trying to increment the int value of the player ID rather than the ID itself. In Java 5+, you can just write playerID++.
As a side note, never ever call Integer's constructor. Take advantage of autoboxing by just assigning ints to Integers directly, like Integer foo = 5. This will use Integer.valueOf(int) transparently, which is superior to the constructor because it doesn't always have to create a new object.
Maybe this is of some worth also: there is a Java class called AtomicInteger.
This class has some useful methods like addAndGet(int delta) or incrementAndGet() (and their counterparts) which allow you to increment/decrement the value of the same instance. Though the class is designed to be used in the context of concurrency, it's also quite useful in other scenarios and probably fits your need.
final AtomicInteger count = new AtomicInteger( 0 ) ;
…
count.incrementAndGet(); // Ignoring the return value.
Java 7 and 8. Increment DOES change the reference, so it references to another Integer object. Look:
@Test
public void incInteger()
{
Integer i = 5;
Integer iOrig = i;
++i; // Same as i = i + 1;
Assert.assertEquals(6, i.intValue());
Assert.assertNotEquals(iOrig, i);
}